Given that $$ar{OP} = \begin{pmatrix}-3 \\ 1\end{pmatrix}$$ and $$\bar{OQ} = \begin{pmatrix}2 \\ 5\end{pmatrix}$$, what is $$\bar{PQ}$$? - HSC - SSCE Mathematics Extension 1 - Question 1 - 2021 - Paper 1

To find the vector $\bar{PQ}$, we use the formula:

$\bar{PQ} = \bar{OQ} - \bar{OP}$.\

Substituting the values, we calculate:

$\bar{PQ} = \begin{pmatrix}2 \\ 5\end{pmatrix} - \begin{pmatrix}-3 \\ 1\end{pmatrix}$

Now, we perform the subtraction:

$\bar{PQ} = \begin{pmatrix}2 - (-3) \\ 5 - 1\end{pmatrix} = \begin{pmatrix}2 + 3 \\ 5 - 1\end{pmatrix} = \begin{pmatrix}5 \\ 4\end{pmatrix}.$

Thus, the vector $\bar{PQ}$ is $\begin{pmatrix}5 \\ 4\end{pmatrix}$.