Question

A particle moves through 3 m due east, 4 m due north and finally 5 m vertically upward. if x,y and z axis are taken along east,north and upward direction respectively.

i) Represent the displacement vector its rectangular components.

ii) Find the magnitude of the resultant displacement.

Answer 1

As per the condition, the particle moves 3m in the east (x-direction),

4 m in the north ( y-direction) and

5 m due in the z-direction

(i) if the movement of the particle is to be speculated in the vectors term then it can be written as

$\overrightarrow{R}=3i+4j+5k$

ii) The question should find the displacement of the particle from the origin,

The net displacement will be $=\sqrt{(3²+4²+5²)}$

$=\sqrt{5}0$

$=7.07$

The displacement is 7.07 units in the direction of vector 3i + 4j + 5k