Find the volume of the parallelepiped defined by the vectors

Solution

The volume of the parallelepiped is:

V = |u.(v x w)|

Thus:

v x w = (3 -5 1) x (3 1 1) = (-6 0 18)

u . (v x w) = (0 2 -2).(-6 0 18) = 0(-6) + 2(0) - 2(18) = -36

So the volume is:

V = |-36| = 36