Find the volume of the parallelepiped determined by the vectors a, b, and c.

a vector = (1,5,3) b vector = (-1,1,5) c vector = (5,1,2)

im not sure if i have to a x (bxc) or the other way around. and answer in cubic units.

The volume is given by any of the three permutations of the scalar triple product:



In fact, the order in which you choose doesn't matter. Although the cross product is anticommutative, i.e. , you end up taking the absolute value anyway, so you'll always have a positive number.

Also, , so really it doesn't matter what order you use, so remembering how to find the volume is easy as long as you know to use a dot and cross product (not two cross products).

You should get a volume of 114 cubic units.