Question

Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 1, 3, 2 , b = −1, 1, 5 , c = 4, 1, 3 in cubic units.

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|.

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 is the vector formed by the edges a and c, C is the vector formed by the edges a and b, and A is the vector formed by the edges b and c.

First, find the cross product of vector B and vector C. Then, take the dot product of the cross product vector with vector A. Finally, take the magnitude of the dot product to find the volume of the parallelepiped.

Answer 2

57 u^3

Step-by-step explanation:

We know that the volume of the parallelepiped determined by the tree vectors is equal to the absolute value of its scalar triple product:

`V = |(a* b)\cdot c|=| \det \left( \left[\begin{array}{ccc}1&3&2\\-1&1&5\\4&1&3\end{array}\right] \right)| = |1(3-5) - 3(-3-20)+2(-1-4)| = |-2+69-10|=|57|=57`

Where we used that the scalar triple product of three vectors equals the absolute value of its determinant.

Therefore, the volume of the parallelepiped is: 57 u^3