A bird flies due east through a distance of `100m`, then heading due north by a distance of `50m`, it flies vertically up through a distance of `20m`. Find the position of the bird relative to its initial position.

Explanation

Displacement along east direction , `vec(s)_(1)=100hat(i)`
Displacement along north direction , `vec(s)_(2)=50hat(j)`
Displacement in upward direction, `vec(s)_(3)=20hat(k)`
The final position `vec(r )` of the bird is followed by three successive displacement `vec(s)_(1)`, `vec(s)_(2)` and `vec(s)_(3)`
`vec(r)=vec(s)_(3)+vec(s)_(3)+vec(s)_(3)=100 hat(i)+50 hat(j)+20 hat(k)`
Then , `|vec(r)|=sqrt(100^(2)+50^(2)+20^(2))=10sqrt(129)m`