How Do You Express Vector C in Terms of A, B, and Theta?

[swooshfactory]

Homework Statement

The question asks to express vector C in terms of A, B, and theta.

Homework Equations

I would guess the relevant equations to be trig equations.

The Attempt at a Solution

I found sin[(180-theta)/2] = k/B (k is a variable I set to equal the right bisected part of C when the angle c was divided in two). Also, sin[(180-theta)/2]= j/A.

c= 180 - theta. After that however, I don't know how to incorporate theta without using phi. Can you assume that a line stretching from the angle to to make a right angle with vector C bisects the angle into two equal angles? That was how I attempted to solve the problem, but I'm not sure if that works. Any help would be greatly appreciated. Thanks in advance.

 

[LowlyPion]

The question asks to express vector C in terms of A, B, and theta.

Homework Equations

I would guess the relevant equations to be trig equations.

The Attempt at a Solution

I found sin[(180-theta)/2] = k/B (k is a variable I set to equal the right bisected part of C when the angle c was divided in two). Also, sin[(180-theta)/2]= j/A.

c= 180 - theta. After that however, I don't know how to incorporate theta without using phi. Can you assume that a line stretching from the angle to to make a right angle with vector C bisects the angle into two equal angles? That was how I attempted to solve the problem, but I'm not sure if that works. Any help would be greatly appreciated. Thanks in advance.

I think you are letting your trigonometry get ahead of your vector addition.

I would suggest developing equations for the x and y components of A and B that would serve to yield C.

For simplicity I might suggest letting C lie along the x-axis. Then you know the y-components of the A and B vectors must sum to 0 and the x will sum to C.

From those equations then look to eliminate any functions of the angle ϕ and leave things in terms of θ.