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

1 Answer
Aug 12, 2016

Answer:

#+-<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>#..