## Problem on finding the volume of a parallelepiped

Sketch and find the volume of the parallelepiped spanned by the vectors $\bfi, \bfi+\bfj,$ and $\bfi + \bfk.$
• ## Solution

We sketch the three vectors:
The parallelepiped spanned by them is:
Recall that
It doesn't matter which vector is $\bfa, \bfb$ or $\bfc$, so we choose them so that the cross product is easier to compute.
Let $\bfa = \bfi + \bfj$, and $\bfb = \bfi$, and $\bfc = \bfi + \bfk.$
The volume of the parallelepiped is 1.