Question

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

For any vectors f\({\rm{u}}\)and\({\rm{v}}\)in\({{\rm{V}}_{\rm{3}}}\),\({\rm{k(u}} \cdot {\rm{v) = (ku)}} \cdot {\rm{v}}\)

Short answer

The answer for the given statement isTRUE.

Step-by-step solution

Dot Product.

\({\rm{u}} \cdot {\rm{v = |u||v|sin\theta }}\)

Where \({\rm{\theta }}\) is the angle between two vectors

The dot product is given by

\({\rm{(ku)}} \cdot {\rm{v}}\)

Here \({\rm{ku}}\) is parallel to\({\rm{u}}\), the angle between \({\rm{ku}}\) and \({\rm{v}}\) is \(\theta \)

Properties of Dot Product.

By property of vector,

Therefore, it can be written as

Thus, the given statement is TRUE.