Question

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)?

Answer 1

`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)`