Answer:
[√3/3, -√3/3, √3/3]^T
Explanation:
You want a unit vector that is orthogonal to both u= [1,1,0]^T and v = [-1,0,1]^T.
Orthogonal
The cross product of two vectors gives one that is orthogonal to both.
w = u×v = [1, -1, 1]^T
Unit vector
A vector can be made a unit vector by dividing it by its magnitude.
w/|w| = [1/√3, -1/√3, 1/√3]^T = [√3/3, -√3/3, √3/3]^T
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Additional comment
The ^T signifies the transpose of the vector, making it a column vector instead of a row vector.
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