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.

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 )