Question

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

For any three vectors u, v and w with the same number of components,$(\mathbf{u}+\mathbf{v})+\mathbf{w}=\mathrm{\_\_\_\_\_\_\_\_\_}$

Short answer

The required expression is$(\mathbf{u}\mathbf{+}\mathbf{v})+\mathbf{w}\mathbf{=}\mathbf{u}+(\mathbf{v}+\mathbf{w})$; Associative Property

Step-by-step solution

Given information

Three vectors $\mathbf{u}\mathit{,}\mathbf{v}\mathbf{}\mathbf{and}\mathbf{}\mathbf{w}$with same number of components.

Completing the expression

The complete expression may be written as:

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

It is the associative property of addition of three vectors.