Vector A has a magnitude of 2 units and makes an angle of 30∘ with the positive x- axis, Vector B has a magnitude of 6 units and makes an angle of 30∘ with the y- axis(clockwise). Find the magnitude of the resultant of Vector A & -B and also the angle that it makes with Vector A.
Using parallelogram law
Now we know magnitude of resultant is give by the formula
So we have
Now we know to find the angle that it makes with the A vector we have the formula
tanθ=b cosθ(a+b sinθ)
tanθ=6 cos 150∘(2+6 sin 150∘)=−3(2−3√)