Finding Magnitudes of Vectors Using the COMPONENTS Method

[crossxfire2]

I am pretty good at this but this one seems impossible to figure out. Can anyone help?

Vector A has a magnitude of 188 units and points 30 degrees north of west. Vector B points 50 degrees East of North. Vector C points 20 degrees West of South. These three vectors add to give a resultant vector that is zero. Using COMPONENTS method, find the magnitudes of Vector B and Vector C.

Thanks in Advance!

 

[CompuChip]

First of all DRAW A PICTURE.
That's about the first rule in vector problems.

Next, let me give you some small sub-problems to get you started... can you rewrite the directions of A, B and C as angles with respect to the x-axis (i.e. east direction)?
Assuming that |B| and |C| are the magnitudes of vector B and C respectively, can you write down what the x- and y-components (Ax, Ay, Bx, By, Cx, Cy) of the three vectors will be?
What relations between these components follow from the resultant being zero?

 

[crossxfire2]

Thanks for the reply CompuChip. I am finding it difficult to find 2 variables (the magnitudes of B and C) based on a couple of other variables.

My Physics teacher wrote this to help us out.

Rx=Ax+Bx+Cx
=()+()B+()C

Ry=Ay+By+Cy
=()+()B+()C

I understand that this is how the problem reads numerically, but I don't understand how to solve.

 

[crossxfire2]

Ok so I did the problem graphically and obtained the correct answers. I verified these answers by plugging them into the calculator. How would I show my work on paper?

 

[CompuChip]

Officially, you can solve the system of two equations in two unknowns.

Rx=()+()B+()C (*)

Ry=()+()B+()C (**)

For example, you can rewrite equation (**) to an equation for either B, or C, for example: B = (Ry - () - ()C) / (). Then you can replace B in equation (*) and solve the remaining equation in one variable for C.