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Edexcel A-Level Mathematics A2 P4.7.6 Vector Equations of Lines Questions

Practise Edexcel IAL P4.7.6 by forming vector line equations, equating components, and applying geometric conditions to points.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • write r = a + λb from two points or a point and a direction vector
  • equate line components to find parameters, constants or an intersection point
  • use a line parameter with a geometric condition to find possible point coordinates
  • Classify two lines as intersecting, parallel or skew from their vector equations

Edexcel A-Level Mathematics A2 P4.7.6 Vector Equations of Lines Questions question 1

[Maximum number: 1]

The line l1l_1 has equation
r=(23−7)+λ(122)\mathbf r=\begin{pmatrix}2\\3\\-7\end{pmatrix}+\lambda\begin{pmatrix}1\\2\\2\end{pmatrix}
where λ\lambda is a scalar parameter.

The line l2l_2 has equation
r=(23−7)+μ(4−18)\mathbf r=\begin{pmatrix}2\\3\\-7\end{pmatrix}+\mu\begin{pmatrix}4\\-1\\8\end{pmatrix}
where μ\mu is a scalar parameter.

Given that l1l_1 and l2l_2 meet at the point P.

The point Q lies on l1l_1 where λ=6\lambda=6.
Given that point R lies on l2l_2 such that triangle QPR is an isosceles triangle with PQ=PR.

state the coordinates of P

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