Final answer:
The volume of the parallelepiped determined by vectors a, b, and c can be found by computing the absolute value of the scalar triple product (B x C). A, which involves the cross product of b and c, followed by taking the dot product with a.
Step-by-step explanation:
The volume of a parallelepiped determined by the vectors a = <1, -2, 3>, b = <2, 4, 2>, and c = <2, 1, 4> can be found using the scalar triple product, which is computed as the dot product of one vector with the cross product of the other two. In this case, the volume is equal to the absolute value of the scalar triple product (B x C). A.
First, compute the cross product of vectors b and c, then take the dot product of the resulting vector with vector a. The volume is the absolute value of this dot product:
V = |(b x c) · a| = |(<2, 4, 2> x <2, 1, 4>) · <1, -2, 3>|
Without explicitly calculating the cross and dot products in this response, we reaffirm that this mathematical process will give you the volume of the parallelepiped.