Question

Find all the vectors orthogonal to both v and w when V = <1,3,-2> and W=<2,-1,4>

Answer 1

I highly recommend watching this and seeing if that helps

http://www.youtube.com/watch?v=m889nydhPTs

Answer 2

there is only 1 vector (and its negative form) that can be orthogonal to 2 vectors.

This vector is the cross product of V and W

Answer 3

let there be a vector r=ai+bj+ck, where a,b,c are some scalars.
now, it r is perpendicular to w, then their dot product equals to zero.
we get, 2a-b+4c=0 ----> 1
similarly r is also perpendicular to the vector v.
from this, we get, a+3b-2c=0 ---->2

since, k is a parameter, there exists many such vectors perpendicular to both w and v.