U421 V049 W338 Find the cross product U x V x WSolutionWe k

U=(4,2,-1) V=(0,4,-9), W=(3,3,8)

Find the cross product: U x ( V x W)

We know that:

Ux(VxW) = (U.W)V - (U.V)W

i.i = j.j = k.k = 1

i.j = i.k = j.k = 0

So,

U.W = (4i + 2j - k).(3i + 3j + 8k)

= 12 + 6 - 8 = 10

U.V = (4i + 2j - k).(0i + 4j - 9k)

= 0 + 8 + 9 = 17

Now

Ux(VxW) = 10*V - 17*W

= 10*(0i + 4j - 9k) - 17*(3i + 3j + 8k)

Ux(VxW) = - 51 i - 11 j - 226 k