Question

Fill in the blanks:

For any vectors u and vin${\mathrm{ℝ}}^3$and any scalar c,$c(\mathit{u}\times \mathit{v})=\_\_\_\_\_\_\_\_=\_\_\_\_\_\_\_\_$

Short answer

The required expression is$c(\mathit{u}\times \mathit{v})=\left(c\mathit{u}\right)\times \mathit{v}=\mathit{u}\times \left(c\mathit{v}\right)$

Step-by-step solution

Given information

Given two vectors u and v in${\mathrm{ℝ}}^3$and a scalarc.

Filling in the blanks

As per the multiplication of a scalar with a cross product:

$c(\mathit{u}\times \mathit{v})=\left(c\mathit{u}\right)\times \mathit{v}=\mathit{u}\times \left(c\mathit{v}\right)$