Find Magnitude and Angle of Vector A with Vector B & C

[cdphys]

Homework Statement

Q1)
Let vector B = (5.00m, 65°), let the magnitude of vector C equal (=) the magnitude of vector A, and C has a direction 20° greater than vector A.
A(dot/scalar product)B = 22.0m^2
B(dot/scalar product)C = 39.0m^2

Find magnitude of A and its direction (angle)?

Homework Equations

Bx = Bcosθ
By = Bsinθ
Trig

The Attempt at a Solution

For Q1 I have tried a variety of methods. To obtain a few angles or magnitudes but I am literally stuck, not even sure where to start. I tried to find the angle between B and C to obtain the Magnitude of C which will equal A... afterwards find the angle between A and B with the newly found magnitude (A = C). Maybe that is the wrong approach, but I could not figure out how to find Mag of C without Cx or Cy...

I am not sure how else to transcribe the math I have on paper to this forum, but if this is lacking information a hint in the right direction would be truly appreciated.

Thanks a lot,
Cd

 

[Joffan]

As a hint, one definition of dot product is: $$ A \cdot B=\left\|A\right\| \, \left\|B\right\| \cos \theta $$, where $\theta$ is the angle between the two vectors. I would look for $\theta$ first.

 

[dimension10]

Homework Statement

Q1)
Let vector B = (5.00m, 65°), let the magnitude of vector C equal (=) the magnitude of vector A, and C has a direction 20° greater than vector A.
A(dot/scalar product)B = 22.0m^2
B(dot/scalar product)C = 39.0m^2

Find magnitude of A and its direction (angle)?

Homework Equations

Bx = Bcosθ
By = Bsinθ
Trig

The Attempt at a Solution

For Q1 I have tried a variety of methods. To obtain a few angles or magnitudes but I am literally stuck, not even sure where to start. I tried to find the angle between B and C to obtain the Magnitude of C which will equal A... afterwards find the angle between A and B with the newly found magnitude (A = C). Maybe that is the wrong approach, but I could not figure out how to find Mag of C without Cx or Cy...

I am not sure how else to transcribe the math I have on paper to this forum, but if this is lacking information a hint in the right direction would be truly appreciated.

Thanks a lot,
Cd

Like Joffan said, for vectors a andb, $\mathfrak R\left(\vec a\cdot\vec b\right)=\left\|a\right\| \, \left\|b\right\| \cos \theta$

 

[SammyS]

Hello cdphys. Welcome to PF !

 

[dimension10]

Actually, it was Joffan who posted that helpful tip.

Oops! I edited my post!