Question

A body moves 6 meters north east and 10 meter vertically upward the resultant displacement of body from its initial position is

Answer 1

The displacement would be √(6^2+8^2+10^2).=10√2 m.

Method 1 ( for magnitude as well as direction of displacement).

Let i,j,k represent unit vectors in x,y,z axis.

Initially the body was at origin so it's position vector was R1= 0i+0j+0k.

After the motion the position vector is R2=8i+6j+10k.

Therefore displacement vector( change in position vector) becomes R=R2-R1

R=8i+6j+10k

Magnitude of displacement vector is given by √(8^2+6^2+10^2)=10√2 m.

The direction( angle made with each axis ) can be found out from the displacement vector.