Question

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

For any vectors u and v, and any scalar k,$k(\mathbf{u}·\mathbf{v})=\_\_\_\_\_\_\_=\_\_\_\_\_\_\_$

Short answer

The required expression is $k(\mathbf{u}·\mathbf{v})=\left(k\mathbf{u}\right)·\mathbf{v}=\mathbf{u}.k\left(\mathbf{v}\right)$; Associative property

Step-by-step solution

Given information

Any vectors u and v, and any scalar k.

Completing the expression 

The expression may be completed as:

$k(\mathbf{u}·\mathbf{v})=\left(k\mathbf{u}\right)·\mathbf{v}=\mathbf{u}.k\left(\mathbf{v}\right)$

It is an example of Associative Property.