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

1 Answer
A. S. Adikesavan
Jul 5, 2016

+-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)

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