Question

Find the volume of the parallelepiped determined by the vertices (0, 1, 0), (1, 1, 1), (0, 2, 0), (3, 1, 2)

Answer 1

The volume of the parallelopiped is 1 cubic units.

In this question,

A parallelepiped is a three-dimensional shape with six faces, that are all in the shape of a parallelogram. It has 6 faces, 8 vertices, and 12 edges. The volume of a parallelepiped is the space occupied by the shape in a three-dimensional plane.

Let the parallelepiped be PQRS.

The vertices of parallelepiped are P(0, 1, 0), Q(1, 1, 1), R(0, 2, 0), S(3, 1, 2).

The volume of parallelopiped can be found by using following steps.

PQ = Q - P = (1,0,1)

PR = R - P  = (0,1,0)

PS = S - P  = (3,0,2)

Now, the volume of parallelopiped is

$v=\left\begin{vmatrix}1&0&1\\0&1&0\\3&0&2\end{vmatrix}$

The determinant the matrix is

⇒ 1(2-0) - 0(0-0) + 1(0-3)

⇒ 1(2) - 0 + (-3)

⇒ 2 - 3

⇒ -1

Hence we can conclude that the volume of the parallelopiped is 1 cubic units.

Learn more about parallelopiped here

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