Question

Find the volume of the parallelepiped determined by the vectors a, b, and c. Given a = (1, 4, 2), b = (-1, 1, 5), and c = (3, 1, 5).

Answer 1

To find the volume of a parallelepiped determined by the vectors a, b, and c, we can use the scalar triple product.

Step-by-step explanation:

To find the volume of a parallelepiped determined by the vectors a, b, and c, we can use the scalar triple product. The scalar triple product is defined as the dot product of two vectors crossed with a third vector.

The scalar triple product of vectors a, b, and c can be calculated as:

V = (a x b) · c

Substituting the given values of vectors a, b, and c, we get:

a = (1, 4, 2), b = (-1, 1, 5), c = (3, 1, 5)

Performing the cross product and dot product, we can calculate the volume:

V = ((1, 4, 2) x (-1, 1, 5)) · (3, 1, 5)

After performing the calculations, the volume of the parallelepiped is 14.