Edexcel FP1 2022 June — Question 3

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2022
SessionJune
TopicVectors: Cross Product & Distances

  1. With respect to a fixed origin \(O\), the points \(A\) and \(B\) have coordinates \(( 2,2 , - 1 )\) and ( \(4,2 p , 1\) ) respectively, where \(p\) is a constant.
For each of the following, determine the possible values of \(p\) for which,
  1. \(O B\) makes an angle of \(45 ^ { \circ }\) with the positive \(x\)-axis
  2. \(\overrightarrow { O A } \times \overrightarrow { O B }\) is parallel to \(\left( \begin{array} { r } 4
    - p
    2 \end{array} \right)\)
  3. the area of triangle \(O A B\) is \(3 \sqrt { 2 }\)