Need help solving for unknown components

[blazeuofa]

Homework Statement

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.

Homework Equations

The magnitude of A= sqrt 5

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

I cannot figure out how to solve this problem. Please help!

 

[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.

 

[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.

 

[blazeuofa]

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.

yes that's what i mean. What would be the result of adding those? That's where I am stuck

 

[rl.bhat]

yes that's what i mean. What would be the result of adding those? That's where I am stuck

Then follow the post 2.Or
R^2 = A^2 + B^2 +2A.B and solve for alpha

 

[blazeuofa]

what do you get when you square B?

 

[Feldoh]

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

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

Just solve for a...

 

[rl.bhat]

1 + a^2