Question

Express the vector u as a sum of two vectors u1 and u2, where u1 is parallel to the vector v and u2 is perpendicular to v

u = (5,-1,-10) v=(2,3,2). I know how to get the perpendicular vector, but its not coming out right when I put it together!

Answer 1

let me try, let say u2 =<x, y, z> which is perpendicular to v. From this, we have u2\(\bullet\)v = 0 . 2x + 3y +2z =0
are you with me now?

Answer 2

I am waiting for your reply, cannot step up if you don't get the first step.

Answer 3

Oh yes of course!

Answer 4

Thats what I did too

Answer 5

It is easiest to find u2 (parallel to vector v)
in fact u2 will be vector v, scaled to the correct length.

if you normalize v to unit length, then find the projection of u onto it

\[ u_2= \left( \frac{u \cdot v}{|v|} \right) \frac{v}{|v|} \]