Review question

# How can we show that $P, Q$ and $R$ are collinear? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9575

## Suggestion

1. A vector of magnitude $OP$ in the direction from $O$ to $P$ is represented by $\mathbf{OP}$. If $\mathbf{OP}-3\mathbf{OQ}+2\mathbf{OR}=\mathbf{0}$, show that $P$,$Q$,$R$ are collinear.

If three points $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are collinear, can we find a connection between $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$?

1. A unit vector parallel to the $x$-axis is represented by $\mathbf{i}$ and a unit vector parallel to the $y$-axis by $\mathbf{j}$. If $\mathbf{OP}=a\mathbf{i}+s\mathbf{j}$ and $\mathbf{OQ}=-a\mathbf{i}+t\mathbf{j}$, where $a$ is a constant and $s$ and $t$ are variables, show that the loci of $P$ and $Q$ are parallel straight lines. In this case find $\mathbf{OQ}$ when $\mathbf{OP}=2\mathbf{i}+3\mathbf{j}$ and $OQ$ is perpendicular to $OP$.

Can we draw a helpful diagram? What is the gradient of each line? What do we know if two lines are perpendicular?