Question

Vector A has a magnitude of 6.0 m and points 30 south of east. Vector B has a magnitude of 4.0 m and points 30° west of south. The resultant vector A B is given by

Answer 1

Magnitude of the vector A = 6m

Magnitude of the vector B = 4m

Angle between the vectors A and B is (30+30)=60°

Now the sum of the vectors A + B =?

$(A+B)^2= A^2 + B ^2 + 2*A* B * cos ( 60�)$

$(A+B)^2= 6^2 + 4^2 + 2*6*4*cos(60)$

$(A+B)^2= 36+16+48*1/2$

$(A+B)^2= 52+24= 76$

$(A+B)= (76)^1/2 = 8.717 m$