Question

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

Answer 1

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).