OCR C4 2011 June — Question 6

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2011
SessionJune
TopicVectors 3D & Lines

6
4 \end{array} \right) + s \left( \begin{array} { l } 3
2
1 \end{array} \right) \quad \text { and } \quad \mathbf { r } = \left( \begin{array} { l } 1
0
0 \end{array} \right) + t \left( \begin{array} { r } 0
1
- 1 \end{array} \right)$$ respectively.
  1. Show that \(l _ { 1 }\) and \(l _ { 2 }\) are skew.
  2. Find the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\).
  3. The point \(A\) lies on \(l _ { 1 }\) and \(O A\) is perpendicular to \(l _ { 1 }\), where \(O\) is the origin. Find the position vector of \(A\). 6 Find the coefficient of \(x ^ { 2 }\) in the expansion in ascending powers of \(x\) of $$\sqrt { \frac { 1 + a x } { 4 - x } } ,$$ giving your answer in terms of \(a\).