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
$O A^{2} = O B^{2} + A B^{2}$
$O A^{2} = 3^{2} + 4^{2}$
$O A^{2} = 25$
OA = 5
So in general $\sqrt{x^{2} + y^{2}}$ is the modulus of the vector with coordinates (x,y).

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

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).