Mathematics

Problem

Statement I If three points

P, Q

and

R

have position vectors

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

respectively, and

2\mathbf{a} + 3\mathbf{b} - 5\mathbf{c} = 0

, then the points

P, Q

and

R

must be collinear. Statement II If for three points

A, B

and

C

\mathbf{AB} = \lambda \mathbf{AC}

, then points

A, B

and

C

must be collinear.