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

Answer:

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:

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

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