Question

Find the volume of the parallelepiped determined by \(u=<2,4,-1>\), \(v=<0,-3,2>\), and \(w=<-1,1,5>\).

Short answer

The volume of the parallelepied is \(39\) cu units.

Step-by-step solution

Given Information

The given vectors are \(u=<2,4,-1>\), \(v=<0,-3,2>\), and \(w=<-1,1,5>\).

The volume of the parallelepiped is \(|(u\times v)\cdot w|\).

Find the cross product of two vector

First, find the \(u\timesv\).

\(\begin{align*}u\times v&= \begin{vmatrix}i&j&k\\2&4&-1\\0&-3&2\end{vmatrix}\\&=5i-4j-6k\end{align*}\)

Find the volume

\(\begin{align*}V&=|(5i-4j-6k)\cdot (-i+j+5k)|\\&=|-5-4-30|\\&=39\end{align*}\)