AQA Further Paper 1 2023 June — Question 9

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
Year2023
SessionJune
TopicVectors: Cross Product & Distances

9 The position vectors of the points \(A , B\) and \(C\) are $$\begin{aligned} & \mathbf { a } = 2 \mathbf { i } + \mathbf { j } + 2 \mathbf { k }
& \mathbf { b } = - \mathbf { i } - 8 \mathbf { j } + 2 \mathbf { k }
& \mathbf { c } = - 2 \mathbf { j } \end{aligned}$$ respectively.
9
  1. Find the area of the triangle \(A B C\)
    9
  2. The points \(A , B\) and \(C\) all lie in the plane \(\Pi\) Find an equation of the plane \(\Pi\), in the form \(\mathbf { r } \cdot \mathbf { n } = d\)
    \(\mathbf { 9 ( c ) } \quad\) The point \(P\) has position vector \(\mathbf { p } = \mathbf { i } + 4 \mathbf { j } + 2 \mathbf { k }\)
    Find the exact distance of \(P\) from \(\Pi\)