Question

Compute the volume of the parallelepiped determined by \(u=i\), \(v=2j\), and \(w=2k\).

Short answer

The volume of the parallelepiped is \(4\) cu units.

Step-by-step solution

Given Information

The three vectors are \(u=i\), \(v=2j\), and \(w=2k\).

A parallelepiped form by these vectors. The volume of parallelepiped is given by,

\(V=|(u\times v)\cdot w|\).

Find the volume of parallelepiped

Substitute \(u\times v=2k\) and \(w=2k\) into formula.

\(\text{Volume }=|2k\cdot 2k|\)

\(\text{Volume }=4\)