The co-ordinates of the point where the line through $\mathrm{A}(3,4,1)$ and $\mathrm{B}(5,1,6)$ crosses the $x y$-plane are

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Aicharya · Accepted Answer

Let $\mathrm{A}\left(x_1, y_1, \mathrm{z}_1\right)=\mathrm{A}(3,4,1)$ $\mathrm{B}\left(x_2, y_2, z_2\right)=\mathrm{B}(5,1,6)$
The equation of line passing through the points $\left(x_1, y_1, z_1\right)$ and $\left(x_2, y_2, z_2\right)$ is given by $\begin{array}{ll} & \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1} \\ \therefore & \frac{x-3}{5-3}=\frac{y-4}{1-4}=\frac{z-1}{6-1} \\ \therefore & \frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-1}{5} \end{array}$
Since the line crosses the XY plane, $\mathrm{z}=0$ $\therefore \quad \frac{x-3}{2}=\frac{y-4}{-3}=\frac{-1}{5}$ $\therefore \quad \frac{x-3}{2}=\frac{-1}{5}$ and $\frac{y-4}{-3}=\frac{-1}{5}$ $\Rightarrow x=\frac{13}{5}$ and $y=\frac{23}{5}$ Required point is $\left(\frac{13}{5}, \frac{23}{5}, 0\right)$

The co-ordinates of the point where the line through $\mathrm{A}(3,4,1)$ and $\mathrm{B}(5,1,6)$ crosses the…

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