How do you find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (4, 0, 2), Q = (7, 3, 5), and R = (7, 3, 8)?

1 Answer
Cesareo R.
Sep 30, 2016

vec n = (1/sqrt(2),-1/sqrt(2),0)

Explanation:

The plane normal is proportional to

vec v = (P-Q) xx (R-Q) = {-9,9,0} so

vec n = lambda vec v now choosing lambda = -1/sqrt(9^2+9^2+0^2) we have

vec n = (1/sqrt(2),-1/sqrt(2),0)

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