Edexcel P4 2021 June — Question 7

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2021
SessionJune
TopicVectors: Cross Product & Distances

  1. Relative to a fixed origin \(O\), the line \(l\) has equation
$$\mathbf { r } = \left( \begin{array} { r } 1
- 10
- 9 \end{array} \right) + \lambda \left( \begin{array} { l } 4
4
2 \end{array} \right) \quad \text { where } \lambda \text { is a scalar parameter }$$ Given that \(\overrightarrow { O A }\) is a unit vector parallel to \(l\),
  1. find \(\overrightarrow { O A }\) The point \(X\) lies on \(l\).
    Given that \(X\) is the point on \(l\) that is closest to the origin,
  2. find the coordinates of \(X\). The points \(O , X\) and \(A\) form the triangle \(O X A\).
  3. Find the exact area of triangle \(O X A\).