The point $A$ has coordinates $\left( 0,\ 2,\ -3 \right)$. The line $l$ has equation $\frac{x}{2}=\f

Question

The point $A$ has coordinates $\left( 0,\ 2,\ -3 \right)$. The line $l$ has equation $\frac{x}{2}=\frac{y+1}{-3}=\frac{z-2}{1}$. Find the cartesian equation of the plane $\pi $ which contains $A$ and is perpendicular to $l$. [3] Hence, or otherwise, find the coordinates of the point $P$ on $l$ which is closest to $A$. [3] The line $m$ passes through the point with coordinates $\left( 4,\ -5,\ 10 \right)$ and $P$. The line $n$ lies in the same plane as $l$ and $m$. Find a cartesian equation for $n$ if $n$ is the reflection of the line $m$ in the line $l$. [6]

Accepted Answer

(a) 2x - 3y + z = -9; (b) P(-2, 2, 1); (c) -(x+2)/6 = (y-2)/11 = (z-1)/3

N2023 Specimen Paper P1 Q10

N2023 Specimen Paper P1 Q10

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