Another operation with vectors is the scalar triple product, defined to be u • (v × w), for vectors u, v, and w in R³.

a. Consider the parallelepiped (slanted box) determined by the position vectors u, v, and w (see figure). Show that the volume of the parallelepiped is the absolute value of the scalar triple product |u • (v × w)|.

b. Use the scalar triple product to find the volume of the parallelepiped determined by the vectors u = (3, 1, 0), v = (2, 4, 1), and w = (1, 1, 5).

Transcribed Image Text:

Ju cos 0