Question

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)?

Answer 1

`=(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 )`