# Need help solving for unknown components

1. Jan 24, 2009

### blazeuofa

1. The problem statement, all variables and given/known data
Vector A = (2x-y)m and Vector B= (x+ay)m (a is alpha, m is meters)

If |A+B|=5m, determine the possible values of a.

2. Relevant equations

The magnitude of A= sqrt 5

3. The attempt at a solution

|A^2 + B^2|=5^2
|(2x-y)^2 + (x+ay)^2|= 5^2
|(2x-y)^2 + (x+ay)^2|= 25

2. Jan 24, 2009

### rl.bhat

Vector A = (2x-y)m and Vector B= (x+ay)m (a is alpha, m is meters)

This statement is not clear. Here what is x and y? Are they equivalent i and j?
If that is the case, find cos(theta) between A and B using dot product. Use this cos(theta) in R^2 = A^2 + B^2 +2AB*cos(theta) to get values of alpha.

3. Jan 24, 2009

### Feldoh

I'm a little confused by your notation, do you mean:

A = <2, -1>; B = <1, a>?

If so add the vectors then take the magnitude and solve for a it should get you a quadratic, I think.

4. Jan 24, 2009

### blazeuofa

yes thats what i mean. What would be the result of adding those? That's where im stuck

5. Jan 24, 2009

### rl.bhat

R^2 = A^2 + B^2 +2A.B and solve for alpha

Last edited: Jan 24, 2009
6. Jan 24, 2009

### blazeuofa

what do you get when you square B?

7. Jan 24, 2009

### Feldoh

A+B = <3, (a-1)>

$$|A+B| = \sqrt{9 + (a-1)^2} = 5$$

Just solve for a...

8. Jan 24, 2009

1 + a^2