Intersections and distances involving planesAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

How do you find where a line meets a plane?
What does it mean if substitution gives 0t=5?
What does it mean if substitution gives 0t=0?
Condition for a line to be parallel to a plane?
Distance from (x1,y1,z1) to ax+by+cz=d?
Distance from point \mathbf p to plane \mathbf r\cdot\mathbf n=d?
How do you find the foot of the perpendicular from a point to a plane?
How do you find the reflection of a point in a plane?
Distance from (1,2,0) to 2x-y+2z=9?
Where does (1+2t,\ -2+t,\ 3-t) meet 3x-y+2z=17?
Why must the modulus be used in the distance formula?
How can you check an intersection point?

Exam questions on Intersections and distances involving planes

The plane $\Pi$ has equation $2x-y+2z=9$ and the point $A$ has coordinates $(1,2,0)$ .
Find the coordinates of the image of $A$ when it is reflected in $\Pi$ .2 marks
The line $l$ has equation $\mathbf r=\begin{pmatrix}1 \\ -2 \\ 3\end{pmatrix}+t\begin{pmatrix}2 \\ 1 \\ -1\end{pmatrix}$ and the plane $\Pi$ has equation $3x-y+2z=17$ .
The line $m$ has equation $\mathbf r=\begin{pmatrix}0 \\ 1 \\ 1\end{pmatrix}+s\begin{pmatrix}1 \\ -1 \\ -2\end{pmatrix}$ . Show that $m$ does not meet $\Pi$ .2 marks
The line $L$ has equation $\dfrac{x-1}{2}=\dfrac{y+3}{1}=\dfrac{z-2}{-3}$ and the plane $\Pi$ has equation $x-2y+z=3$ .
Find the coordinates of the point where $L$ meets $\Pi$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).