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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

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Question 1

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.png

Given that $$ar{OP} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$$ and $$\bar{OQ} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$$, what is $$\bar{PQ}$$?

Worked Solution & Example Answer: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

Step 1

Calculate vector $$\bar{PQ}$$

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Answer

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

PQˉ=OQˉ−OPˉ\bar{PQ} = \bar{OQ} - \bar{OP}.

Substituting the given vectors, we have:

PQˉ=(25)−(−31)\bar{PQ} = \begin{pmatrix} 2 \\ 5 \end{pmatrix} - \begin{pmatrix} -3 \\ 1 \end{pmatrix}.

This simplifies to:

PQˉ=(2+35−1)=(54).\bar{PQ} = \begin{pmatrix} 2 + 3 \\ 5 - 1 \end{pmatrix} = \begin{pmatrix} 5 \\ 4 \end{pmatrix}.

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