2021 YIJC P2 Q4
The line $l$ has equation $\frac{x+1}{2}=\frac{y-a}{b}=\frac{z-4}{3}$. The plane$~p$ has equation $x+y-z-11=0$.
(i)
If $l$ and $~p$ do not intersect, what can be said about the values of $a$ and $b$?
[3]
For the rest of the question, use $a=-2$ and $b=1$.
(ii)
Find the coordinates of the point $B$, the foot of perpendicular from the point $A\left( -1,a,4 \right)$ to $p$.
[2]
(iii)
Hence, or otherwise, find a vector equation of the line of reflection of $l$ in $~p$.
[2]
(iv)
Find the possible position vectors of the point $C$ on $l$ which is a distance of $\sqrt{164}$ from $B$.
[3]
(v)
Find the angle $BCA$.
[2]
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