(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

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# Homework Help: Find vector parallel to yz plane and perpendicular to other given vector

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