A body moves 6m north 8 metre east and 10 metre vertically upward what is the resultant displacement from initial position

Let us take positive x axis in east.

Then x component of displacement is 8 m.

We take positive y axis in north. Then,

y component of displacement is 6 m.

We take positive z axis in vertically upward direction. This gives

z component of displacement is 10 m.

The displacement vector is (8,6,10) m

The magnitude of this vector is (64+36+100)^(1/2)=(200)^(1/2)=10 sqrt 2.

When you travel 6m North and 8m East, in 2 dimensions the resultant vector by Pythagoras theorem is 10m.

From that point it travels 10m upwards which again forms a right angle triangle in a different plan from the resultant vector whose magnitude is also 10m

Therefore again applying Pythagoras theorem, root of 10^2 + 10^2 = 10