orthogonal vectors?

Question

If a= i +6j+k and b= i+13j+k , find a unit vector with positive first coordinate orthogonal to both a and b.
____i + ____ j + _____k

Answer 1

The following 3 by 3 determinant will get you the vector that is orthogonal to both a and b

i.... j.....k
1 ..6....1
1...13...1

Then find the length of the resulting vector and divide the vector by the length to get the unit vector.

Oh, and if the first coordinate of the resulting vector is not positive, just multiply each component by -1

Answer 2

If you take the cross product of b and a you get

(b X a) = 7i - 7k
Has a positive first coordinate and is orthogonal to both a and b.

The unit vector would be
(i - k)/√2