Can you help me find a unit vector that is orthogonal to both [1, 1, 0] and [1, 0, 1]?
1 Answer
Feb 6, 2018
Explanation:
The cross product of two vectors is orthogonal to both:
#[1, 1, 0] xx [1, 0, 1] = abs((hat(i), hat(j), hat(k)), (1, 1, 0), (1, 0, 1)) = [1, -1, -1]#
Note that the dot product of this vector with either of the two original vectors is
Now to make it of unit length, we need to divide it by its norm:
#abs("["1, -1, -1"]") = sqrt(1^2+(-1)^2+(-1)^2) = sqrt(3)#
So a suitable unit vector is:
#1/sqrt(3) [1, -1, -1] = [sqrt(3)/3, -sqrt(3)/3, -sqrt(3)/3]#