Pearson Edexcel IAL Mathematics P4.7.6 Vector equations of lines

Practise forming vector equations of lines, using parameters to locate points, and testing intersections, parallel lines and geometry constraints.

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

[Maximum number: 1]

The line $l_1$ has equation
$\mathbf r=\begin{pmatrix}2\\3\\-7\end{pmatrix}+\lambda\begin{pmatrix}1\\2\\2\end{pmatrix}$
where $\lambda$ is a scalar parameter.

The line $l_2$ has equation
$\mathbf r=\begin{pmatrix}2\\3\\-7\end{pmatrix}+\mu\begin{pmatrix}4\\-1\\8\end{pmatrix}$
where $\mu$ is a scalar parameter.

Given that $l_1$ and $l_2$ meet at the point P.

The point Q lies on $l_1$ where $\lambda=6$ .
Given that point R lies on $l_2$ such that triangle QPR is an isosceles triangle with PQ=PR.

state the coordinates of P

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P4.7.6 - Vector equations of lines question 1