Find the area of ΔPQR. P(3, −2, 6), Q(−1, −4, −6), R(3, −8, 6)

Question

Find the area of ΔPQR.

P(3, −2, 6),   Q(−1, −4, −6),   R(3, −8, 6)

Answer 1

Vector PQ = <- 4, - 2, - 12>.

Vector PR = <0, - 6, 0>.

Cross product PQ×PR = det{(i j k) (- 4 - 2 - 12) (0 - 6 0)] = - 72i + 24k.

Area of ΔPQR = 1/2IIPQ×PRII = 1/2√72² + 24² = 12√10