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.