Question

A particle has displacement 12m east, 5m towards north and 6m vertically upwards. Find the magnitude and sum of these displacements.

Answer 1

let us first calculate the displacement for 12m and 5m.
R1=sqrt(12^2 +5^2)
     = sqrt(169)
     =13m
Now calculate for R1 and 6m vertically upward.
R2=sqrt(13^2 + 6^2)
     =sqrt(205)
     =14.32m
so resultant displacement is 14.32m
Note ^ means raised to power

Answer 2

East, North along the ground and Vertically upwards (above ground)  are mutually perpendicular directions.

so net displacement = √(12² + 5² + 6²) m = √205 m

The direction will be like the principal diagonal of the cuboid.