Question

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

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

Short answer

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

Step-by-step solution

Given information

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

Completing the expression

The expression may be complete as:

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

It is distributive property of cross product.