Question

Fill in the blanks:

If u, v, and w are vectors in ${\mathrm{ℝ}}^3$, then ______ is the volume of the parallelepiped determined by u, v, andw.

Short answer

The required expression is$\left|\mathit{u}.(\mathit{v}\times \mathit{w})\right|$

Step-by-step solution

Given information

Three vectors u, v, and w in${\mathrm{ℝ}}^3$.

Filling in the blanks

The volume of parrallelepiped is given by$\left|\mathit{u}.(\mathit{v}\times \mathit{w})\right|$