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

To find ( \overrightarrow{PQ} ), we use the formula:

$\overrightarrow{PQ} = \overrightarrow{OQ} - \overrightarrow{OP}$

Substituting the values we have:

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

Calculating the difference:

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

Thus, ( \overrightarrow{PQ} = \begin{pmatrix} 5 \ 4 \end{pmatrix} ). This corresponds to option C.