Mathematics

Problem

For three distinct points

P, Q, R

with position vectors

\mathbf{p}, \mathbf{q}, \mathbf{r}

, which of the following conditions is sufficient to ensure that

P, Q, R

are collinear? a)

(\mathbf{q}-\mathbf{p})\cdot(\mathbf{r}-\mathbf{q}) = 0

(\mathbf{q}+\mathbf{p})\times(\mathbf{r}+\mathbf{q}) = \mathbf{0}

(\mathbf{q}-\mathbf{p})\times(\mathbf{r}-\mathbf{q}) = \mathbf{0}

|\mathbf{q}-\mathbf{p}| = |\mathbf{r}-\mathbf{q}|