Question

Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)

Required:
Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Answer 1

Answer: the vector orthogonal is ( 0, 26, -13 )

Explanation:

Given that;

P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)

PQ = Q - P = (−2, 1, 4) - (2, 0, 2) = (-4, 1, 2)

PR = R - P = (7, 2, 6) - (2, 0, 2) = ( 5, 2, 4)

SO

orthogonal vector = PQ × PR

= ║ i j k

-4 1 2 = i(1×4 - 2×2) + j(5×2 - (-4×4)) + k(-4×2 - 5×1) = 0i + 26j - 13k

5 2 4 ║

= ( 0, 26, -13 )

Therefore the vector orthogonal is ( 0, 26, -13 )