Mathematics

Problem

Two displacement vectors are given by

\mathbf{p}=\langle 2,3,-1\rangle

and

\mathbf{q}=\langle -1,4,2\rangle

. Use these data to answer the questions that follow. a. (i) Calculate

\mathbf{p}\!\cdot\!\mathbf{q}

. b. (ii) Determine the magnitudes

|\mathbf{p}|

and

|\mathbf{q}|

. c. (iii) Hence find the angle between

\mathbf{p}

and

\mathbf{q}

, giving your answer correct to the nearest degree.