Dividing line segments

If the point \(P\) divides the line segment \(AB\) in the \(m:n\), then:

\(\overrightarrow{OP} = \overrightarrow{OA} + \dfrac{m}{m+n}\overrightarrow{AB} \)

\(\quad = \overrightarrow{OA} + \dfrac{m}{m+n}(\overrightarrow{OB} - \overrightarrow{OA}) \)



Comparing coefficients

If \(\bold{a}\) and \(\bold{b}\) are not parallel vectors, and \(p\bold{a} + q\bold{b} = r\bold{a} + s\bold{b} \),

then \(p=r\) and \(q=s\).

Mechanics

In mechanics, vector quantities, such as velocity, displacement and force, have both magnitude and direction.

Speed is the magnitude of a velocity vector.

Distance is the magnitude of a displacement vector.