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