Multiplication of vector problem

[Adrianw2]

Homework Statement

Let B = 5.00m at 60 degrees. Let C have the same magnitude as A and a direction angle greater than that of A by 25.0 degrees. Let A*B = 30.0 m^2 and B*C = 35.0 m2. Find A.

Homework Equations

Pythagoras maybe.

The Attempt at a Solution

Well, if A*B is 30 m^2, and B is 5.00m, then shouldn't A = 6.0 m? However, I don't think it's that easy, so I made the right angle triangle with B (5.0m) as the hypotenuse at 6 meters above the horizontal, and got 4.33m as the opposite and 2.5m as the adjacent. Am I going to be calculating areas of triangles? I'm not really sure where to go from there.

Thanks

 

[Hootenanny]

I'm assuming the astericks denote the scalar product? I think your going to have to set up a system of simulatenous equations.

 

[Adrianw2]

Yeah, the astericks are actually a dot, so it may have something to do with the dot product where it's AxBx + AyBy or something along those lines.

 

[Hootenanny]

Yeah, the astericks are actually a dot, so it may have something to do with the dot product where it's AxBx + AyBy or something along those lines.

I suggest you write out two equations using \theta to denote the unknown angle.