Mathematics

Problem

Let

\mathbf{a}

and

\mathbf{b}

be two non–zero vectors. a. (i) Write the geometric definition of the scalar (dot) product of

\mathbf{a}

and

\mathbf{b}

. b. (ii) Using this definition, explain why the condition

\mathbf{a}\cdot\mathbf{b}=0

is equivalent to the angle between

\mathbf{a}

and

\mathbf{b}

being

90^{\circ}

. c. (iii) If

|\mathbf{a}|=5,\;|\mathbf{b}|=7

and

\mathbf{a}\cdot\mathbf{b}=0

, state whether

\mathbf{a}

and

\mathbf{b}

can be parallel. Give a brief reason for your answer.