Question

Use matrices to find the volume of the parallelepiped formed by the three given vectors: a = ⟨2, -3, 6⟩ b = ⟨4, 2, 1⟩ c = ⟨-2, 1, 5⟩

Answer 1

102

Explanation:

To find the volume of a parallelepiped using matrices, you can arrange the three vectors as columns of a 3x3 matrix.

`\left[\begin{array}{ccc}2&4&-2\\-3&2&1\\6&1&5\end{array}\right]`

Now, you simply find the determinant, and that gives you the volume. The determinant of this matrix is 102.