What is the unit vector that is orthogonal to the plane containing <0, 4, 4> and <1, -1, 1> ?

1 Answer
Douglas K.
Jan 14, 2017

Compute the cross product of the to vectors.
Compute the magnitude of the resulting vector.
Divide the resulting vector by its magnitude.
The unit vector is: < sqrt(6)/3, sqrt(6)/6, -sqrt(6)/6>

Explanation:

Compute the cross product:

<0,4,4>xx <1,-1,1> = | (hati,hatj,hatk), (0,4,4), (1,-1,1) | = 8hati + 4hatj - 4hatk

Compute the magnitude:

r = sqrt(8^2 + 4^2 + (-4)^2)

r = sqrt(96) = 4sqrt(6)

The unit vector is: < sqrt(6)/3, sqrt(6)/6, -sqrt(6)/6>

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