How do you find the direction of a vector given its magnitude and angle?

[egadda2]

Homework Statement

Vector A points in the negative x direction. Vector B points at an angle of 33.0 degrees above the positive x axis. Vector C has a magnitude of 13 m and points in a direction 37.0 degrees below the positive x axis.

Given that , Vector A + Vector B + Vector C = 0, find the magnitudes of Vector A and Vector B.

Homework Equations

The Attempt at a Solution

 

[Fightfish]

Construct a vector diagram. You should get a closed triangular loop from the three vectors.

 

[Mark44]

Homework Statement

Vector A points in the negative x direction. Vector B points at an angle of 33.0 degrees above the positive x axis. Vector C has a magnitude of 13 m and points in a direction 37.0 degrees below the positive x axis.

Given that , Vector A + Vector B + Vector C = 0, find the magnitudes of Vector A and Vector B.

Homework Equations

The Attempt at a Solution

Let a = the magnitude of A = |A|
Let b = |B|
Let c = |C| = 13 (given)

Write the three vectors in terms of their coordinates, like this:
A = -a*i + 0*j
B = b*cos(33 deg)*i + b*sin(33 deg)*j
C = 13*cos (-37 deg)*i + 13*sin(-37 deg)*j

For the three vectors to sum to zero, their horizontal components have to add to zero, and their vertical components have to add to zero. Set up these two equations and solve for the unknowns a and b. Once you have these values you can find the magnitudes of A and B.