The line $l$ has equation $\frac{x+2}{-2}=\frac{y-1}{4}=\frac{z-3}{6}$. Find the coordinates of

Question

The line $l$ has equation $\frac{x+2}{-2}=\frac{y-1}{4}=\frac{z-3}{6}$. Find the coordinates of the points on $l$ that are of distance $\sqrt{11}$ from the point $\left( 0,0,3 \right)$.[4] The plane $\pi $ has equation $\mathbf{r}\cdot \left( \mathbf{i}-2\mathbf{j}-3\mathbf{k} \right)=1$. Show that $l$ is perpendicular to $\pi $.[1]

Accepted Answer

The points are $(-1,-1,0)$ and $\left(-\dfrac{17}{7},\dfrac{13}{7},\dfrac{30}{7}\right)$. Also, $l\perp\pi$.

2011 CJC P1 Q10 [Modified]

2011 CJC P1 Q10 [Modified]

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