Question

How do I find the magnitude with two coordinates ?

Answer 1

Let the direction are given as follows

$+x = east$

$-x = west$

$+y = North$

$-y = South$

now for the above displacement

it moves east for 5 m so it is

$x_1 = 5$

then goes north for 3 m

$y_1 = 3$

then goes west for 2 m

$x_2 = -2 m$

now total displacement in East or x direction

$x = x_1 + x_2 = 5 - 2 = 3m$

total displacement in North of Y direction

$y = 3m$

so final coordinates are

$x = 3, y = 3$

Part b)

position vector is given as

$r = x\hat i + y\hat j$

$r = 3\hat i + 3\hat j$

so the magnitude of the vector is given as

$|r| = \sqrt{3^2 + 3^2}$

$|r| = 3\sqrt3$