







The line of intersection of two planes 
20151209 

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. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul Answered by Penny Nom. 





An equilateral triangle with vertices in 3 parallel planes 
20140531 

From prajay: How to construct an Equilateral Triangle whose vertices lie on three
parallel lines, if the distances of two lines are 'a' and 'b' units
from the middle line.What is the length of the side of the
Equilateral Triangle ? Answered by Chris Fisher. 





If x+y+z=1 then x^2 + y^2 + z^2 = ? 
20140430 

From Nitin: If x+y+z=1
then
x^2 +y^2+z^2 = ? ? Answered by Robert Dawson. 





The distance from a point to a line in 3 space 
20061029 

From Marie: find the distance from the point (1, 2, 3) to the line x = y = z2 Answered by Penny Nom. 





Vectors in three space 
20041030 

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. 





Distance in 3space 
20020816 

From David: The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = 8.213, and z = 11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. Answered by Penny Nom. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley. 





A line in 3 dimensions 
20011017 

From Murray: I'm working on a complicated proof and i need the equation for a line in 3 dimensions. Answered by Claude Tardif. 

