Two position vectors in metres are given by and with respect to the origin of an –…

PHYSICS · Subjective · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two position vectors in metres are given by

\mathbf{r}_1=(6,-2)

and

\mathbf{r}_2=(-3,4)

with respect to the origin of an

x

–

y

coordinate system. (i) Derive a general component‐wise expression for the displacement vector

\Delta\mathbf{r}=\mathbf{r}_2-\mathbf{r}_1

in terms of the components of

\mathbf{r}_1

and

\mathbf{r}_2

. (ii) Using a convenient scale, draw

\mathbf{r}_1

and

\mathbf{r}_2

from the origin and then obtain

\Delta\mathbf{r}

by graphical construction. (iii) On the same sketch mark the vector

-\Delta\mathbf{r}

. Measure the length of both

\Delta\mathbf{r}

and

-\Delta\mathbf{r}

and comment on your observation. (iv) Compute the exact magnitude of

\Delta\mathbf{r}

from its components and compare this value with your measurement.