Solving Vectorial Equation: F vs a Angle Relationship

[PLuz]

Hi everyone,

I was wondering, if I have this vetorial equation:\vec{F}\cdot\vec{v}=\vec{a}\cdot\vec{v}
I can say that F\cos (\theta)=a\cos (\phi),where \theta and \phi are the angles that \vec{F} and \vec{a} do with the vector \vec{v}, respectively.

The doubt is: does Sign(\cos (\theta))=Sign(\cos (\phi))? Because F and a represent the modulus so have to be positive, right?

Thank you

 

[Khashishi]

I think it's
F\cos (\theta)=a\cos (\phi),
I'm not sure where the sin came from.

 

[PLuz]

Yeh it's \cos, I was distracted. I'm going to change it. Thank you.

 

[nasu]

Hi everyone,

The doubt is: does Sign(\cos (\theta))=Sign(\cos (\phi))? Because F and a represent the modulus so have to be positive, right?

Thank you

If the equality is true, then the signs of the cosines must be the same.