Question

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?

Answer 1

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