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Tim Gan Math

2003 A-Level H2 Mathematics

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Question 5Vectors6 marks

Referred to the origin \(O\) , the position vectors of points \(A\) and \(B\) are \(4\mathbf{i}-11\mathbf{j}+4\mathbf{k}\) and \(7\mathbf{i}+\mathbf{j}+7\mathbf{k}\) respectively.

  1. Find a vector equation for the line \(l\) passing through \(A\) and \(B\) .[2]
  2. Find the position vector of the point \(P\) on \(l\) such that \(OP\) is perpendicular to \(l\).[4]
Solution step 1, image 1
Solution step 2, image 1

Final Answer:

(i) \(\mathbf r=\begin{pmatrix}7 \\ 1 \\ 7\end{pmatrix}+\lambda\begin{pmatrix}1 \\ 4 \\ 1\end{pmatrix}\), \(\lambda\in\mathbb R\). (ii) \(\overrightarrow{OP}=\begin{pmatrix}6 \\ -3 \\ 6\end{pmatrix}\).