If u = 3i + j + 4k, v = -i + 2j, and w = - 2i - 3j + 5k, evaluate u . (v × w).

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Quizplus · Accepted Answer

The cross product of vectors v and w, v × w, is calculated first. Then, the dot product of vector u and the result of v × w is found.v = -i + 2j, w = -2i - 3j + 5kv × w = |i  j  k |         |-1  2  0|         |-2 -3  5|= i(2*5 - 0*(-3)) - j((-1)*5 - 0*(-2)) + k((-1)*(-3) - 2*(-2))= 10i + 5j + (3 + 4)k= 10i + 5j + 7kNow, u . (v × w) = (3i + j + 4k) . (10i + 5j + 7k)= 3*10 + 1*5 + 4*7= 30 + 5 + 28= 63

If U = 3i + J + 4k, V =