Question

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

Answer 1

To find the volume of the parallelepiped determined by the vectors a, b, and c, you can use the formula V = |(B x C) . A|, where B and C are two of the given vectors and A is the remaining vector. Substituting the given values, the volume is 49 units cubed.

Step-by-step explanation:

To find the volume of the parallelepiped determined by the vectors a, b, and c, we can use the formula V = |(B x C) . A|, where B and C are two of the given vectors and A is the remaining vector.

To find the cross product of B and C, we can use the formula B x C = (B2C3 - B3C2, B3C1 - B1C3, B1C2 - B2C1).

Substituting the given values for a, b, and c, we have B x C = (3, 17, 6).

Finally, substituting the cross product and the vector A into the formula for volume, we get V = |(3, 17, 6). (1, 2, 2)| = |(3 + 34 + 12)| = |49| = 49 units cubed.