Question

Find a unit vector perpendicular to a=(4,-3,1) and b=(2,3,-1)


What I did:
a x b = ((-3)(-1)-(3)(1), (1)(2)-(-1)(4), (4)(3) - (2)(-3))
=(0,6,18)

Answer is (0, 1/square root 10, 3/square root 10)

Answer 1

your initial vector is correct

magnitude of (0,6,18) = √(0+36+324) = √360
= 6√10
so I see that your unit vector is also correct

Perhaps you are looking at some answer key and the answer there looks different.
They might have rationalized the denominator

1/√10
= 1/√10 *√10/√10
= √10/10

3/√10 = 3√10/10

alternate form of your unit vector:
(0 , √10/10 , 3√10/10 )