Find the perpendicular Vector?

Question

Given the vectors u=(0, -2, 1) and v=(1, 0, 3), find the vector perpendicular to both u and v

Answer 1

Cross product gives required vector:-

| i"""""j"""""k |
|0""""-2""""1|
|1""""0"""""3|

- 6i + j + 2k is perpendicular to vectors u and v.

Answer 2

Okay, I think with i,j,k being vector, then i0-2j+k=0 and
i+0j+3k=0.
So, lets multiply first equation by -3, giving you 6j-3k=0.
And add i+3k=0, giving you 6j+i=0, or i=-6j.
And you know that k=2j.
So, just plug in any number in i,j, or k.
Well, just let i=1.SO, 1=-6j, so, j=-1/6.
And k=2*(-1/6)=-1/3.
So, that gives you (1,-1/6,-1/3), or to get all whole numbers,
multiply by 6, giving you (6,-1,-2).

Answer 3

Try doing a cross-product on the two vetors.