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Question

The magnitude of the position vector of the point (3, 4) will be ___

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Solution

The position vector of the point with coordinates as (3,4) on a x-y plane will look like

To calculate its modulus i.e., length of OA, use Pythagoras theorem in triangle OAB
OA2=OB2+AB2
OA2=32+42
OA2=25
OA = 5
So in general x2+y2 is the modulus of the vector with coordinates (x,y).

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