Mathematics

Problem

(i) State the algebraic condition that two non–zero vectors

\mathbf{a}

and

\mathbf{b}

must satisfy to be perpendicular and prove the statement. (ii) State the algebraic condition that two non–zero vectors

\mathbf{a}

and

\mathbf{b}

must satisfy to be parallel (or anti-parallel) and prove the statement. (iii) Write one explicit pair of non-zero vectors in

\mathbb R^{3}

that are perpendicular and another explicit pair that are parallel, verifying each condition by direct computation.