A hiker follows three successive displacement vectors: due east

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

A hiker follows three successive displacement vectors:

\mathbf{p}=4\,\text{km}

due east,

\mathbf{q}=3\,\text{km}

due north and

\mathbf{r}=2\,\text{km}

due west. (i) Write

\mathbf{p},\;\mathbf{q},\;\mathbf{r}

in unit-vector form. (ii) Compute

(\mathbf{p}+\mathbf{q})+\mathbf{r}

. (iii) Compute

\mathbf{p}+(\mathbf{q}+\mathbf{r})

. (iv) Explain the equality of the two results obtained in (ii) and (iii). (v) Analyse whether adding in the order

\mathbf{q}+\mathbf{p}+\mathbf{r}

affects the resultant and state the underlying principle.