Use the given vectors to find the indicated expression.
-v = 2i + 2j + 2k, w = -4i - 3j + 4k, u = 5i + 2j + 5k Find u · (v × w).
A) 48
B) 24
C) 58
D) -24

Question

Quizplus · Accepted Answer

To find u · (v × w), first calculate the cross product v × w = (2i + 2j + 2k) × (-4i - 3j + 4k) = (2(4) - 2(-3))i - (2(4) - 2(-4))j + (2(-3) - 2(-4))k = (8 + 6)i - (8 + 8)j + (-6 + 8)k = 14i - 16j + 2k. Then, calculate the dot product u · (v × w) = (5i + 2j + 5k) · (14i - 16j + 2k) = 5(14) + 2(-16) + 5(2) = 70 - 32 + 10 = 48.

Use the Given Vectors to Find the Indicated Expression