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?

1 Answer
Dec 29, 2015

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

Explanation:

Vector A =13[cos250i+sin250j]=-4.446i-12.216j
Vector B =27[cos330i+sin330j]=23.383i-13.500j

Vector A + B =18.936i-25.716j

Magnitude A+B =sqrt(18.936^2+(-25.716)^2)=31.936

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

Reference Angle =tan^-1(25.716/18.936)=53.6^o

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

Hope that helped