[b]uDividing line segments[/u]/b

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}) )

mtaimg/images/topics/10/10-109-1.png/mtaimg

[b]uComparing coefficients[/u]/b

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).

[b]uMechanics[/u]/b

In mechanics, bvector quantities/b, such as velocity, displacement and force, have both magnitude and direction.

bSpeed/b is the magnitude of a velocity vector.

bDistance/b is the magnitude of a displacement vector.