Question

For any vectors \({\rm{u}}\)and \({\rm{v}}\)in\({{\rm{V}}_{\rm{3}}}{\rm{,}}\)\({\rm{|u}} \cdot {\rm{v| = |u||v|}}\).

Short answer

The given statement is False.

Step-by-step solution

Evaluation.

Use the formula, already know that,

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

Therefore,

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

The given statement is true only when\({\rm{sin\theta = 1}}\).

Vectors direction.

When two vectors are perpendicular to one other, this occurs.

For all other cases, the given statement is not true.

Therefore, the given statement is False.