2022 EJC J2 MCT Q8
Planes $p$ and $q$ have equations $x+y+z=5$ and $3x+y-z=9$ respectively, and meet in the line $l$.
(a)
Find a vector equation for $l$.
[2]
(b)
Verify that the point $A$ with position vector $\mathbf{i}+\mathbf{j}+3\mathbf{k}$ lies on $p$.
[1]
(c)
Find the position vector of $F$, the foot of perpendicular from $A$ to $q$. Hence find the coordinates of $A’$, the reflection of the point $A$ about $q$.
[5]
(d)
The point $B$ lies on the line segment $AA’$. The plane $r$ contains the line $l$ and the point $B$. Find the range of values for $\theta $, the acute angle between $r$ and $q$.
[3]
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