# Finding Length of a Vector

1. Aug 31, 2010

### sami23

1. The problem statement, all variables and given/known data
Find the length of the vector C starting from the components given in Equations 3 and 4.
Express C in terms of A, B, and theta.

2. Relevant equations
3. Cx= A + Bcos($$\theta$$),
4. Cy = Bsin($$\theta$$).

3. The attempt at a solution
C = $$\sqrt{C_x ^2+C_y ^2}$$
C = $$\sqrt{A^2+(Bcos\theta)^2+(Bsin\theta)^2}$$
using trig identity cos2 $$\theta$$+sin2 $$\theta$$=1
C = $$\sqrt{A^2+2B^2}$$ ???

2. Aug 31, 2010

### CompuChip

You have all the right ingredients, but be careful!

$$(A + B \cos\theta)^2$$ is not the same as $$A^2 + (B \cos\theta)^2$$.

This is a classical trap... (x + 1)² is not equal to x² + 1²... to see what it does equal, you can write it out as (x + 1)(x + 1) and expand the brackets.

3. Aug 31, 2010

### sami23

C = $$\sqrt{A^2 + 2ABcos\theta + B^2}$$

4. Aug 31, 2010

### CompuChip

Now you're just sloppy and maybe guessing a bit, aren't you? :)