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| = √(3^2 + 3^2)`

`|r| = 3\sqrt3`