### Scalar multiplication

of vectors, changes the magnitude of the vector but not the direction.

For scalar $$a$$ and vector $$\vec{A}$$ with

x- or horizontal component $$A_H=A \cos \theta$$

y- or vertical compnonet $$A_V= A \sin \theta$$

magnitude $$A=\sqrt{A_H^2 + A_V^2}$$

The multiplication $$a \times \vec{A}$$ has magnitude $$a \times A$$.

The division $$\vec{A} \div a$$ has magnitude $$A \div a$$.