Edexcel A-Level Mathematics A2 P4.7.5 Distance Between Two Points Questions

Practise Edexcel IAL P4.7.5 by applying the 3D distance formula to line parameters and finding all possible point positions.

Exam points

Set up a squared length equation to find possible parameters or positions on a line

[Maximum number: 3]

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.

find the coordinates of the possible positions of point R

Attempts a correct method of finding at least one value for $\mu$ , for example
$(4\mu)^2+\mu^2+(8\mu)^2=6^2+12^2+12^2, \quad \mu=\pm2$
Attempts one correct position:
$\mathbf r=\begin{pmatrix}2\\3\\-7\end{pmatrix}\pm2\begin{pmatrix}4\\-1\\8\end{pmatrix}$
Possible coordinates are (10,1,9) and (-6,5,-23).

All question bank results loaded

Edexcel A-Level Mathematics A2 P4.7.5 Distance Between Two Points Questions question 1