A Body moves 6 m north. 8 m east and 10

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A Body moves $6\, m$ north. $8 \,m$ east and $10\;m$ vertically upwards, what is its resultant displacement from initial position

A

$10\sqrt 2 m$

B

$10m$

C

$\frac{{10}}{{\sqrt 2 }}\,m$

D

$10 \times 2\,m$
A Body moves $6\, m$ north. $8 \,m$ east and $10\;m$ vertically upwards, what is its resultant displacement from initial position
$\vec r = x\hat i + y\hat j + z\hat k$
$\therefore r = \sqrt {{x^2} + {y^2} + {z^2}} $
$r = \sqrt {{6^2} + {8^2} + {{10}^2}} = 10\sqrt 2 \;m$