Find the magnitude of a vaector a and the smallest postive a

Find the magnitude of a vaector a and the smallest postive angle from the x axis to vector OP (-2,-2sqrt(3))

Solution

given (-2,-2sqrt(3))

magnitude r=[(-2)²+(-23)²]

r =[4+12]

r=16

r =4

= +tan^-1((23)/2)

= +tan^-13

= +(/3)

=4/3=240⁰