How do you find all unit vectors that is orthogonal to the plane through the points P = (3, -3, 0), Q = (5, -1, 2), and R = (5, -1, 6)?

1 Answer
A. S. Adikesavan
Jul 27, 2016

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

Explanation:

Vector PQ = ( 5, -1, 2 ) - ( 3, -3, 0 ) = ( 2, 2, 2).

Vector QR = ( 5, -1, 6 ) - ( 5, -1, 2 ) = ( 0, 0, 4)

Vector +-PQ X QR = ( 8, -8, 0 ) is normal to the plane PQR.

So, the unit orthogonal vectors are

+- (( 8, -8, 0 ))/ | ( 8, -8, 0 ) |

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

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