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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
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