Find the magnitude and direction in degrees of the vector As

Find the magnitude and direction (in degrees) of the vector. (Assume 0° < 360°.)

v = 15i + 5sqrt3j

Solution

v = 15i + 5sqrt3 *j

Now magnitiude   |v| = sqrt( 15^2 (5sqrt3)^2 )

= 10sqrt3

Angle : tan(theta) = 5sqrt3/15 = sqrt3/3

theta = pi/3 = 60 degres