I learned that we can get the component of a vector in any direction using the dot product. The problem I have is the meaning of the term component itself. The component of a vector $\vec A$ in the direction of the unit vector $\vec u$ is $$|\vec A||\vec u|\cos (\theta).$$
1) Will the other component be $|\vec A|\cos (90-\theta)$?
2) Do any two components must be perpendicular or can they be any two vectors whose sum will be vector $\vec A$?
3) If the angle $\theta$ between vector $\vec A$ and the unit vector that indicates the direction of the component I want is $90 <\theta<180$
The component will have a negative sign
Does this sign mean that no component in the direction of the unit vector and that the only component will be in the opposite direction?