Question

How do you find a vector perpendicular to the plane containing (0,0,1), (1,0,1) and (-1,-1,-1)?

Answer 1

`+-<0, 2, -1>`.

Explanation:

The vector `+-PQ X PR` is perpendicular to the plane containing

`P(0. 0. 1), Q(1. 0. 1) and R(-1, -1, -1)`.

If O is the origin the vectors `OP. OQ, OR` are #<0, 0, 1>, <1, 0, 1>

and <-1, -1, -1>#.

Now, #pQ=OQ-OP= <1. 0, 0>

and PR = OR-OP = <-1. -1, -2>#

`+-PQ X PR =+-<(0)(-2)-(0)(-1), (0)(-1)-(1)(-2), (1)(-1)- (0)(-1)>`

`=+-<0, 2, -1>`..