Find the magnitude and direction angle of the vector 4 squar

Find the magnitude and direction angle of the vector (-4 squareroot 3, -4) The magnitude of the vector is (Simplify your answer.)

Solution

We have given vector v=<x,y>=<-4sqrt(3),-4>

magnitude of the vector is ||v||==sqrt((-4sqrt(3))^2+(-4)^2)=sqrt(48+16)=sqrt(64)=8

tan(theta)=y/x

theta=arctan((-4)/(-4*sqrt(3)))=arctan(1/sqrt(3))

theta=30⁰

magnitude of the vector is 8 and the direction angle is 30⁰