The plane $p$ passes through the points with coordinates $\left( -k,2,5 \right)$, \(\left( 0,2,-

Question

The plane $p$ passes through the points with coordinates $\left( -k,2,5 \right)$, $\left( 0,2,-1 \right)$ and $\left( -\frac{1}{2},3,-1 \right)$, and the line $l$ has equation $\frac{x+2}{-3}=y-2=\frac{z-4}{k}$, where $k$ is a constant. Show that the cartesian equation of the plane is $6x+3y+kz=6-k$.[2] Show that the $l$ cannot be perpendicular to $p$.[2] For the rest of this question, let $k=-2$. Given that $l$ meets $p$ at point $N$, find the coordinates of $N$.[3] Another plane $\pi $ is parallel to the plane $p$. Given that the distance between $p$ and $\pi $ is $11$ units, find the possible points of intersection between $l$ and $\pi $.[3]

Accepted Answer

(iii) ${N(4,0,8)}$ (iv) ${(-17,7,-6)}$ and ${(25,-7,22)}$

2021 MI P2 Q4

2021 MI P2 Q4

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