Magnitude of a vector?

A vector has a magnitude of 188 units and points 30.0deg north of west. Vector B points 50deg east of north. Vector C points 20deg west of south. These three vectors add to give a resultant vector that is zero. Using components, find the magnitude of vector B and vector C

Magnitude of a vector?
It will help if you draw out the vector to know what direction they are pointing at, so that you can determine whether the components are postive or negative.





Let's b and c denote the magnitude of Vector B and vector C:





Components of Vector A: (-188 cos 30) i + (188 sin 30) j





Components of Vector B: (b sin 50) i + (b cos 50) j





Components of Vector C: (- c cos 20) i + (- c sin 20) j





Since the resultant vector is a zero vector, it implies the summation of i component and j component of Vector A, B, C are zero.





i component:





0 = -188 cos 30 + b sin 50 - c cos 20





j component:





0 = 188 sin 30 + b cos 50 - c sin 20








Solve the two equations simultaneously:





you will get:





b = -95.45





c = 95.45