Physics

Problem

A hiker starts from the origin

O

. Step 1: He walks to point

A

so that his position vector becomes

\mathbf{r}_1 = 4\hat{i}-3\hat{j}\,\text{km}

. Step 2: From

A

he reaches point

B

whose position vector with respect to

O

\mathbf{r}_2 = -2\hat{i}+5\hat{j}\,\text{km}

. Step 3: From

B

he finally moves to point

C

by a further displacement

\mathbf{d}=6\hat{i}+2\hat{j}\,\text{km}

relative to

B

. (a) Write the position vector of point

C

with respect to

O

. (b) Find the magnitude of the hiker’s total displacement from

O

C

. a. (a) Position vector of

C

b. (b) Magnitude of total displacement