Question

Fill in the blanks:

Let u and v be nonzero vectors in${\mathrm{ℝ}}^3$with the same initial point. Thenrole="math" localid="1653202810378" $||\mathit{u}\times \mathit{v}||=\_\_\_\_\_\_\sin \theta$ where θ is _____.

Short answer

The required expression is$||\mathit{u}\times \mathit{v}||=||\mathit{u}||||\mathit{v}||\sin \theta$,$\theta$is the angle between u and v.

Step-by-step solution

Given information

Two vectors u and v with the same initial point in${\mathrm{ℝ}}^3$

Filling in the blanks

The blanks may be filled as under:

$||\mathit{u}\times \mathit{v}||=||\mathit{u}||||\mathit{v}||\sin \theta ,\mathrm{where}\theta$ is the angle between u and v.