A hiker travels from the base camp to point with a displacement vector km and then…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

A hiker travels from the base camp

C

to point

P

with a displacement vector

\mathbf{p}=6\,\hat{i}+2\,\hat{j}+3\,\hat{k}

km and then from

P

to point

Q

with displacement vector

\mathbf{q}=-4\,\hat{i}+7\,\hat{j}+\hat{k}

km. (a) Determine the resultant displacement vector

\mathbf{d}

from

C

Q

. (b) Calculate the magnitude of

\mathbf{d}

. (c) Find the unit vector that gives the direction in which the hiker must travel directly from

C

Q

. (d) If the hiker wishes to return to

C

from

Q

along the shortest path, write the unit vector that represents this return direction.