The discussion revolves around determining the possible values of the variable \( a \) in the context of vector addition and magnitudes. The vectors are defined as \( \mathbf{A} = (2x - y) \) m and \( \mathbf{B} = (x + ay) \) m, with the condition that the magnitude of their sum equals 5 m.
Participants are actively engaging with the problem, clarifying notation and exploring different methods to approach the solution. Some have provided guidance on how to manipulate the vectors and set up equations, but there is no explicit consensus on a single method or interpretation yet.
There is some ambiguity regarding the definitions of \( x \) and \( y \), and whether they correspond to unit vectors in a Cartesian coordinate system. Additionally, the problem's constraints regarding the magnitude of the vectors and the variable \( a \) are under consideration.
Feldoh said: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.
Then follow the post 2.Orblazeuofa said:yes that's what i mean. What would be the result of adding those? That's where I am stuck