Question

Fill in the blanks and give the name of the property.

Let u, v, and w be vectors in ${\mathrm{ℝ}}^3$. Then $\mathbf{u}\times (\mathbf{v}+\mathbf{w})=\_\_\_\_\_\_\_\_\_\_$

Short answer

The required expression is$\mathbf{u}\times (\mathbf{v}+\mathbf{w})=\mathbf{u}\times \mathbf{v}+\mathbf{u}\times \mathbf{w}$; Distributive property

Step-by-step solution

Given information

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

Completing the expression

The complete expression may be written as:

$\mathbf{u}\times (\mathbf{v}+\mathbf{w})=\mathbf{u}\times \mathbf{v}+\mathbf{u}\times \mathbf{w}$

It is an example of Distributive property.