Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1>

Question

Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1>

 

First vector = <?, ?, ?>

Second vector = <?, ?, ?>

Answer 1

a x b is orthogonal to both a and b.  Evaluate a x b and divide by its magnitude to get a unit vector.  Similarly, -a x b is orthogonal to a and b.

 

The 2 unit vectors can be n and -n, where

 

n = (a x b) / |a x b|

 

Do you know how to evaluate a x b?  Can you evaluate |a x b| ?  If so, you should be able to finish from here.