- #1
Raziel2701
- 128
- 0
Homework Statement
Find a vector u that is parallel to the yz-plane and perpendicular to the vector v=<5,0,4>.
2. The attempt at a solution
I first tried to find a unit vector parallel to the yz-plane, I then crossed this vector with vector v, but then I remembered that the resulting vector would be perpendicular to both, so that wouldn't work.
Let me be more precise:
1. I found a unit vector to (0,1,1)
I got (0,1/sqrt(2), 1/sqrt(2))
2. I was going to cross this vector with v (5,0,4) but then I realized that the resulting vector would be perpendicular both the yz plane and vector v so I didn't follow through.
So then :
1. I crossed u(a,b,c) with the yz plane (0,1,1) and got:
(b-c)i -(a)j +(a)k and set it equal to zero because I want them to be parallel.
Clarifying that I'm using a,b, and c as my unknowns.
2.I tried dotting this vector I found with vector v(5,0,4) and I set them equal to zero but now I have an equation with three unknowns but I don't know how to solve them.
Here's what I got:
5b-5c +4a=0