Use ordered pair notation (𝑥, 𝑦) and column vector notation (𝑥 𝑦) to represent a position vector in two dimensions.

Use the diagram below to determine the ordered pair notation for the position vector $\vec{OA}$.

Use column vector notation to express the position vector represented by the ordered pair (−3, 7).

A particle moves from point P(2, 5) to point Q(7, −3). a) Express the position vector of point Q in column vector notation. (1 mark) b) Determine the displacement vector $\overrightarrow{PQ}$ in column vector notation. (1 mark) c) Express the displacement vector $\overrightarrow{PQ}$ using ordered pair notation. (1 mark)

Points A and B have position vectors represented as A(−3, 7) and B(5, −2) respectively. (a) Express the position vector of point A in column vector notation. (1 mark) (b) Determine the displacement vector from A to B, expressing your answer in column vector notation. (1 mark) (c) A point C lies on the line segment AB such that AC = ⅔AB. Use ordered pair notation to express the position vector of point C. (1 mark)