Find the area of the parallelogram with vertices: P(0,0,0), Q(3,-5,5), R( 3,-7,7), S(6,-12,12)

Answer 1

PQ and PR are sides of the parallelogram.

PS is the diagonal since PS = PQ + PR as vectors (the sum of (x,y,z) of Q and R gives S).

Find the vector product of the sides PQ and PR, using any method from your textbook:

PQ x PR = (3,-5,5) x (3,-7,7) = (0, -6, -6)

The parallelogram area will be length of the the vector product:

area = length of (0, -6, -6) = root(0² + 6² + 6²) = 6√2