Topic: vector list of topics
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	Translation by a vector		2020-01-30
		From Jude: M(3,-2) is the image of the point M under a translation by the vector (-5,2). Find the coordinates of M Answered by Penny Nom.
	Vectors		2019-09-06
		From Kayla: Hi! Due to time constraint issues, we skipped vectors in Pre-Calc last year. However, I'm attempting to complete my AP Physics summer homework and there are 3 problems with vectors. As I explained, I have no idea even where to begin and as such I need some help. Problem 1: A plane flying at 90° at 45 m/s is blown toward 0° at 62 m/s by a strong wind. Find the plane's resultant velocity. I have tried all sorts of online calculators but none are providing me with a formula I can use to solve this problem on my own. Problem 2: If you walk 367 m North and 785 m West what is your total displacement from your original location? What is the problem asking for when it says displacement? Problem 3: A plane travels on a heading of 127.0° at a velocity of 25 km/hr. What are the horizontal and vertical components of the plane's velocity? As you know already, I have never done vectors so I don't know what horizontal and vertical components of velocity are. Thank you So Much for your help!! I am struggling!! - Kayla Answered by Penny Nom.
	A range hood		2017-12-04
		From Chuck: I'm building a custom range hood and can't seem to get the angles correct where the front and side panels intersect. I saw a similar post but there's no way I can do the calculations for a Wolfram Alpha! Here are the dimensions that I have (in inches)... Base - Front 29 7/16" x side 19 3/16" Top - Front 10" x side 9" Front Panel Length (from base to top on an angle) 21" Side Panel Length (from base to top on an angle) - 17 9/16" Vertical distance from the base to the top 14 1/4 inches. Any help finding the bevel/miter of the two front corners where the sides meet the front panel would be greatly appreciated. I will need the angle for the saw in degrees. Thank you in advance! Regards, Chuck Answered by Harley Weston.
	The angle between two planes		2017-09-12
		From Arthi: Hello. hope you are having a good day. I am stuck on a maths question in which it is asking, how to find the angle between two given planes. These planes are in a 3D shape such as a prism. How can I do this? Please reply as soon as possible Thank You Answered by Penny Nom.
	Speed and velocity		2016-02-14
		From kechi: A boat sails south through Chesapeake Bay. It takes 10 hours to sail 110 kilometers. Describe the boat's motion. Calculate the boat's speed and velocity, showing the calculations. Explain how the boat's speed is different from its velocity Answered by Penny Nom.
	The line of intersection of two planes		2015-12-09
		From Rabz: Determine the vector equation for the intersection between the two given planes 2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom.
	Column vectors		2015-02-21
		From jill: A has co- ordinates (7,-1) and B has co-ordinates (3,5).write these as column vectors Answered by Penny Nom.
	Vector division		2012-08-28
		From Nazrul: If A and B be two vectors where B = 3 A The What is B/A ? Please help me. Answered by Robert Dawson.
	The position of an aircraft relative to the airport		2012-06-08
		From Dennis: "Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing.  Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north.  What are the x,y, and z components (in meters) of the position vector. The x-axis is east, the y-axis is north and the z-axis is vertical. Answered by Penny Nom.
	A vector geometry problem		2011-10-28
		From aishwarya: hi...my name is Aishwaarya and i am a student from India.. My problem is in vector geometry which i am sending u my an attachment including a diagram.. Thanks Aishwarya Answered by Chris Fisher.
	Building a custom range hood		2011-10-08
		From Bill: I'm building a custom range hood for a customer with special order material that matches their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate the bevel and miter of the three sides but I never was very good with geometry functions (although I am fairly good with other math fields). I either need the calculations from you at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston.
	The length of a vector		2010-09-12
		From kyrie: Find the possible values of the constant a such that | ai + 4aj + 4k | = 13 I know the answer is 3 but not sure how to get to it Answered by Penny Nom.
	The triangle inequality		2010-01-11
		From Nazrul: If A and B are any two vectors, then how can I prove that magnitude of (A+B)<=magnitude of A+magnitude of B. Please show me the process in details. Thank you. Answered by Robert Dawson.
	Two non zero vectors		2009-10-27
		From Nazrul: Given that a and b are two non zero vectors and ma+nb=0 where m and n are two scalars. How can I prove that m=n=0. Answered by Robert Dawson.
	Vector spaces		2009-07-05
		From Nazrul: How can I prove that m(a+b)=ma+mb where a and b are two vectors. Thank you. Answered by Harley Weston.
	Vector Proofs		2009-06-25
		From Nazrul: If a, b, c be three vectors how can I prove that (i) -(a+b)=-a-b (ii) If a+b =c then a= c-b Thank you. Answered by Janice Cotcher.
	Vectors and the Law of Cosine		2009-06-08
		From lauren: once force of 20 pounds and one force of 15 pounds act on a body at the same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces Answered by Janice Cotcher.
	Ground Velocity of an Aircraft		2009-06-07
		From Anna: An aircraft is flying at 180km/hr and there is a northerly wind of 35km/hr. The pilot steers the aircraft at an angle of 40 degree east of north. Which direction (in degrees east of north) is the aircraft travelling over the ground? Answered by Stephen La Rocque.
	An aeroplane flying in a wind		2009-06-02
		From Maria: The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air, are such that its resultant speed and direction are 800 kph, and direction N71.6◦E I need to find the size of the angle between v and vw, in degrees to one decimal place, and find the speed at which the aeroplane would fly if the air were still, to the nearest kph. It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane would have if the air were still, the velocity vw of the wind, and the resultant velocity v of the aeroplane (diagram should be in the form of a triangle illustrating how one velocity vector is the sum of the other two) Thanks Answered by Harley Weston.
	The midpoints of two sides of a triangle		2009-03-17
		From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson.
	Find the resultant of this displacement pair		2009-02-22
		From katydidit: Find the resultant of this displacement pair: 500 miles at 75 degrees east of north and 1500 miles at 20 degrees west of south. How do I graph this and how do I solve this problem? Answered by Penny Nom.
	The path of a small sailboat		2008-11-19
		From jane: a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East then 3.40 km North East, then an additional distance in an unknown direction. Her final position is 6.68 km directly east of the starting point. find the magnitude & direction of the third leg of the voyage. Answered by Harley Weston.
	Vectors and an orientation change in the axes		2008-08-30
		From moumita: what differences take place to a vector because of choice of orientation of the coordinate axes and why?? Answered by Harley Weston.
	A roof angle		2008-08-30
		From carla: Use vectors to find the angle in the attached diagram Answered by Chris Fisher and Stephen La Rocque.
	The flight of an airplane		2008-08-29
		From kobina: You are traveling on an airplane that is moving at 500 mph in a direction 40deg north of west.Therefore , You are travelling (due to the plane ) at how many mph toward the west. Answered by Stephen La Rocque.
	A force vector		2008-08-28
		From moumita: |F|=20N...this force is acting along a vector A=4j+3k.what is F? Answered by Penny Nom.
	3-D Vectors		2008-07-22
		From jenina: 1. The summit of a mountain, 2450m above base camp, is measured on a map to be 4580m horizontally from the camp in a direction 32.4º west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north and z axis up. Answered by Janice Cotcher.
	Two forces acting on a body		2008-06-21
		From Rita: Before answering the question below, what exactly is, in basic words, resultant force? QUESTION: Two forces of 50 and 68 pounds act on a body to produce a resultant force of 70 pounds. Find, to the nearest 10 minutes or nearest tenth of a degree, the angle formed between the resultant force and the smaller force. Answered by Harley Weston.
	A cat is walking on the tread of a tank		2008-05-26
		From Kathleen: If a cat is walking on the tread of a tank travelling at 28kmh how fast does the cat have to walk to avoid falling under the tracks? Answered by Janice Cotcher.
	Scalar triple product and volume of a general tetrahedron		2007-08-03
		From Anurag: how do you prove that volume of tetrahedron= 1/12 times scalar triple product of vectors a,b and c? Answered by Stephen La Rocque.
	The bearings of a ship's journey		2007-07-20
		From sugar: A ship starts from point osail eastward for 6 hours. Then changes its course to N50E for 8 hours and then N62W for 10 hours until it reaches the point c. If the speed of the ship was imi/h, what is the bearing of the side oc? Answered by Harley Weston.
	Rate of change of distance between the clock hands		2007-06-05
		From Jonathan: A certain Clock has a minute hand with a length of 4 inches long and an hour hand with a length of 3 inches long. How fast is the distance between tips of these hands changing at 9:00? Answered by Stephen La Rocque.
	The velocity of an aircraft		2007-03-22
		From William: Hello, I don't understand how to work this problem. Thanks in advance for your help! A jet moving at 500.0 km/h due east moves into a region where the wind is blowing at 120.0 km/h in a direction 30.0 degrees north of east. What is the new velocity and direction of the aircraft relative to the ground? Answered by Penny Nom.
	vectors		2007-02-25
		From harsh: Two vectors U= Uxi -6j +k And V= -3i +Vyj +k. Their dot product U.V= -35. AND the magnitude of their sum is |U+v|= 3. What are the components of Ux and Vy ? Answered by Stephen La Rocque.
	Romeo is throwing pebbles		2007-02-08
		From Jessie: Romeo is chucking pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5m below her window and 5.0m from the base of the wall. How fast are the pebbles going when they hit her window? Answered by Stephen La Rocque.
	An octagonal bird house		2007-01-13
		From Soren: I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew! Answered by Harley Weston.
	Bearings		2006-11-22
		From Suzy: Mr. John wants to fly her airplane from point A to B, a distance of 450 miles. If B has a heading of 60 degrees from A, and there is a constant wind from the southeast blowing at 60 mph, find the speed and heading she should maintain in order to land at B in 90 minutes. Answered by Stephen La Rocque.
	An aircraft going from city A to city B		2006-05-10
		From Preston: An aircraft going from city A to city B on a bearing of S69 degrees East is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the plane's true bearing. Answered by Stephen La Rocque.
	Equations of two lines		2006-04-05
		From Wael: Determine a cartesian equation of the line passing through A and V as a direction vector? 1- A (2;1) and V = j 2- A (2;3) and V = i Answered by Penny Nom.
	Find the ground speed and the planes true heading.		2006-02-05
		From Jimmie: An aircraft going from city A to city B on a bearing of S69E (degrees) is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the planes true heading. Answered by Penny Nom.
	The combined force of two vectors		2004-10-30
		From Brian: Two teams are playing push ball with a large 8 foot diameter ball. One team exerts a force represented by the vector a = 2i + -5j, and the other team exerts a force represented by the vector b = -8i-3j. 1.Determine the direction of movement of the ball if the i axis is due east. 2.Determine the combined force magnitude. Answered by Harley Weston.
	Vectors in three space		2004-10-30
		From Jo: I have two questions that I just cannot visulise and dont know how to get started on them..! 1. Ship X is sailing North at 4m/s and Ship Y is sailing due East at 3m/s. A sailor on Ship X climbs a vertical pole at 1/2 m/s. What is the velocity of the sailor on Ship X relative to an observer on Ship Y? State it's magnitude and direction. Not sure where to start with this one... 2. Show, using vectors, that for any tetrahedron, the segments joining the midpoints of the opposite edges are concurrent. i know what a tetradedron is, and what I am proving but do I solve simultaneously for a specific case?? Answered by Walter Whiteley.
	The force of a 5000 tonne lorry		2004-10-27
		From Aaron: A 50 tonne lorry is parked on a slope with a gradient of 4%. Due to the self weight of the lorry, what is the force * acting down the slope * acting normal (at right angles) to the slope Answered by Penny Nom.
	An aircraft is flying directly from airport A to airport B		2004-10-22
		From A student: In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from airport A to airport B, which is 2000 km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i-30j)km/h. Calculate (i) the time of flight, to the nearest min (ii) the direction of the wind. Answered by Penny Nom.
	Cycling in the wind		2004-10-11
		From A student: A cyclist is travelling in the direction of 12i+5j at a speed of 39 km/h where i is a unit vector due east and j is a unit vector due north. The wind appears to the cyclist to be blowing with a velocity of (-4i+j) km/h. Find, correct to 1 d.p (a) the true speed of the wind and (b) the bearing from which the wind is blowing Answered by Penny Nom.
	A parallelepiped		2004-09-25
		From Aman: " If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,-2), B is (3,6,1), and C is (4,0,-1), find the coordinates of the other vertices of the parallelepiped.)" Answered by Penny Nom.
	Two vector problems		2004-07-14
		From Jaye: Two force, 120lb and 200lb, act on a body and make a 52 degree angle w/ ea. other. What's the magnitude of the resultant of the forces and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force? Answered by Penny Nom.
	The commuter		2004-07-14
		From JJ: A student who commutes 27 mi. to college remembers, after driving a few minutes, he forgot a term paper. Driving faster than usual, he returns home, gets the paper, and once again starts to school. Sketch the graph of the student's distance from home as a function of time. Does it mean that the student drives at normal speed, drives faster to pick up the paper, and resumes normal speed to head back, or that the student drives at normal speed, then drives faster the rest of the way to college? Answered by Penny Nom.
	Vectors		2004-07-06
		From Annie: a=3i-j+2k and b=i+3j-2k, determine the magnitude and direction cosines of the product vector and show that it is perpendicular to a vector c=9i+2j+2k. Answered by Chris Fisher.
	Arc length		2002-04-17
		From Vix: Find the point on the curve r(t)=(12sint)i-(12cost)j+5tk at a distance 13pi units along the curve from the point (0,-12,0) when t=0 in the direction opposite to the direction of increasing arc length. Answered by Harley Weston.
	Adding vectors		2002-01-12
		From Lena: how do you add vectors together? If you are given the length and angles of both vectors and are asked to add/subtract them, how do you do it? I know you are supposed to do the head to tail method, but whenever i try it i get the wrong answer. I need help setting it up. example: A is 2.7cm, and 60 degrees, B is 1.6cm and 135 degrees, find the magnitude and amplitude Answered by Penny Nom.
	Translated by the vector (-5,2)		2001-11-19
		From Jennifer: Give the image of (p,q) when translated by the vector (-5,2). Answered by Penny Nom.
	Multiplying vectors		2001-10-22
		From Murray: Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b) Answered by Harley Weston.
	The speed of the boat		2001-07-12
		From Sharon: A motor boat is travelling in a southeasterly direction in water that is flowing from the south at 2km per hour. Show that the speed of the boat is (6 times the square root of 2) km per hour, given that it can travel at 10km per hour in still water. Answered by Penny Nom.
	Vector Problem		2000-11-27
		From Ben: An aircraft can fly 260km/h in still air and the wind is blowing at 70km/h towards the West. In what direction should the aircraft head so that its actual velocity is on a bearing of 030 degrees? Answered by Harley Weston.
	The angle of rotation		2000-08-03
		From Jay: I have the following information Given. (X1, Y1) Origional Point (X2, Y2) Origional Point After a Rotation (Xa, Xb) Center of Rotation What formula would I use to figure out the angle the point was rotated? Answered by Chris Fisher and Harley Weston.
	Area of a triangle from vertex coordinates		1999-04-21
		From Mark Tyler: I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too. I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula: A = abs((x1-x2)*(y1-y3)-(y1-y2)*(x1-x3)) for triangle (x1,y1)(x2,y2)(x3,y3) I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long. Regardless, it may be fun for the kids, even if it's not on the curriculum. Answered by Walter Whitley.
	Finding the Mine		1997-06-23
		From Billy Law: Tom is gold prospector. On his last trip out from town, he headed 35 degree South of West to a lake where he had lunch. The lake was 24 km out of Town. He then headed due East for 35 km before Doubling back on bearing of 15 degree South of west for 20 km to reach his mine. By converting to Cartesian coordinate before doing vector additions do the following: a) Calculate the position of the mine from town in term of a distance and a direction. ... Answered by Harley Weston.
	Le terme		2003-04-01
		From Francine: Je suis une enseignante de 5e/6e et j'aimerais savoir comment on traduit le terme "array" en français. Answered by Claude Tardif.
	Espaces vectoriels		2002-08-18
		From Bacar: Comment montrer que trois (ou plus que trois) sous espaces vectoriels sont en somme directe. Answered by Claude Tardif.

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