Find two unit vectors orthogonal to both given vectors

[C6ZR1]

Hello,

Could someone please review my work and see if it is correct. Thanks

Homework Statement

Find two unit vectors orthogonal to both given vectors.
i + j + k, 3i + k

Homework Equations

The Attempt at a Solution

So I used cross product and got A x B= i+2j-3k

Then I got magnitude: to be √ (14)

problem asks to rationalize denominator and I eventually get..

lower values: <-√(14)/14 i, -√(14)/7 j, 3√(14)/14 k>

larger values: <√(14)/14 i, √(14)/7 j, -3√(14)/14 k>



I just want to make sure that I did everything correctly.

 

[jbunniii]

Looks right to me. You can verify your answers by checking that their inner (dot) products with both given vectors are zero, and that their lengths are 1.

You really only need to check one answer because you know the second answer has to be the negative of the first.