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

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

[ \bar{PQ} = \bar{OQ} - \bar{OP} ]

Substituting the given values:

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

Performing 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 answer is ( \bar{PQ} = \begin{pmatrix} 5 \ 4 \end{pmatrix} ), corresponding to option C.