   SEARCH HOME Math Central Quandaries & Queries  Question from harsh, a student: 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 ? Hi Harsh.

I've re-written your question using bold face for the vector quantities and regular face for the scalar quantities:

Two vectors U= Ux i -6j +k And V= -3i +Vy j +k. Their dot product UV= -35. AND the magnitude of their sum is |U+V|= 3. What are the components of Ux and Vy ?

The dot product of two three-dimensional vectors is computed by adding together the products of the components in the same direction. In your question, this means

-35 = UV = -3Ux - 6Vy + 1

The sum of these two vectors is simply the vector whose components are the sums of the components in the same direction:

U + V = (Ux - 3)i + (Vy - 6)j + 2k

And the magnitude of any vector is the square root of the sum of the squares of its components, so the magnitude of U + V is:

3 = |U + V| = sqrt( (Ux - 3)2 + (Vy - 6)2 + 22 )

Now you have two equations with two unknowns. Can you finish the question now?

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.