Use ordered triple notation (𝑥, 𝑦, 𝑧) and column vector notation ( 𝑥 𝑦 𝑧) to represent a position vector in three dimensions.

Use column vector notation to express the position vector represented by the ordered triple \((4, -7, 3)\).

Consider the point \(P\) in three-dimensional space located at 4 units along the positive \(x\)-axis, 7 units along the negative \(y\)-axis, and 3 units along the positive \(z\)-axis from the origin. (a) Express the position vector \(\overrightarrow{OP}\) in ordered triple notation. (1 mark) (b) Express the position vector \(\overrightarrow{OP}\) in column vector notation. (1 mark)

Consider the points \(A(2, -3, 5)\), \(B(4, 1, -2)\), and \(C(-1, 3, 7)\) in three-dimensional space. (a) Determine the position vector of point \(B\) in column vector notation. (1 mark) (b) Determine the position vector of the midpoint \(M\) of segment \(AC\) and express your answer in ordered triple notation. (2 marks) (c) Use your answers from parts (a) and (b) to determine the vector \(\vec{BM}\) in column vector notation. (1 mark)