Mathematics

Problem

Consider two non-zero vectors

\vec{p}

and

\vec{q}

. Answer the following questions. a. (i) State the relationship connecting the scalar product of two non-zero vectors, their magnitudes, and the angle between them. b. (ii) Explain what can be concluded about the angle between

\vec{p}

and

\vec{q}

in each of the following cases: (a)

\vec{p}\,\cdot\,\vec{q}>0

, (b)

\vec{p}\,\cdot\,\vec{q}<0

, (c)

\vec{p}\,\cdot\,\vec{q}=0

. c. (iii) Without calculating the actual measure of the angle, classify the angle between the vectors

\vec{r}=2\mathbf{i}-\mathbf{j}+4\mathbf{k}

and

\vec{s}=-3\mathbf{i}+5\mathbf{j}+2\mathbf{k}

as acute, obtuse or right-angled. Justify your answer.

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