# Vector A has a magnitude of 13 units at a direction of 250 degrees and vector B has a magnitude of 27 units at 330 degrees, both measured with respect to the positive x axis. What is the sum of A and B?

Dec 29, 2015

Convert the vectors to unit vectors , then add ...

#### Explanation:

Vector A $= 13 \left[\cos 250 i + \sin 250 j\right] = - 4.446 i - 12.216 j$
Vector B $= 27 \left[\cos 330 i + \sin 330 j\right] = 23.383 i - 13.500 j$

Vector A + B $= 18.936 i - 25.716 j$

Magnitude A+B $= \sqrt{{18.936}^{2} + {\left(- 25.716\right)}^{2}} = 31.936$

Vector A+B is in quadrant IV . Find the reference angle ...

Reference Angle $= {\tan}^{-} 1 \left(\frac{25.716}{18.936}\right) = {53.6}^{o}$

Direction of A+B $= {360}^{o} - {53.6}^{o} = {306.4}^{o}$

Hope that helped