Mathematics

Problem

Consider the vectors

\mathbf{p}=6\hat{i}-2\hat{j}+3\hat{k}

and

\mathbf{q}=-2\hat{i}+\hat{j}+2\hat{k}

. a. (i) Obtain the unit vector in the direction of

\mathbf{q}

. b. (ii) Find the scalar projection (component) of

\mathbf{p}

\mathbf{q}

. c. (iii) Hence determine the vector projection of

\mathbf{p}

\mathbf{q}

. d. (iv) Verify that the sum of the vector projection found in part (iii) and the component of

\mathbf{p}

perpendicular to

\mathbf{q}

equals

\mathbf{p}

itself.