Question

How do you find all unit vectors orthogonal to both the vectors given below: (1,2,-1) and (3,3,-4)?

Answer 1

`+-1/sqrt 35(-5, 1, -3)`

Explanation:

The unit vectors (in opposite directions) that are orthogonal to both

`a and b` is `+-( a X b)/| a X b |`.

Here `a=(1, 2, -1) and b=(3, 3, -4),`

`a X b =((2)(-4)-(3)(-1), (-1)(3)-(-4)(1), (1)(3)-(3)(2))`

`=(-5, 1, -3) and |(-5, 1, -3)| = sqrt 35`.

So, the answer is `+-1/sqrt 35(-5, 1, -3)`