(Hint: What does it represent in the special case where the parallelepiped is a rectangular solid?)
Last week we examined two methods for multiplying vectors, the scalar (dot) product and the vector (cross) product. The scalar product (A .B = ABcosq) yields a scalar whose magnitude indicates the relative alignment of the vectors. The vector product yields another vector whose magnitude indicates the relative perpendicularity of the original vectors and whose direction is perpendicular to both original vectors. There's an interesting combination called the triple scalar product. It is
where f is the angle between B and C and q is the angle between A and the vector created by B x C.
| If vectors A, B and C are "length" vectors that lie exactly along the edges of a parallelepiped, what quantity does the triple scalar product represent? (Hint: What does it represent in the special case where the parallelepiped is a rectangular solid?) | |
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