The line passing through the points (1,2,-1) and (3,-1,2) meets the...

Eqn. of line $\Rightarrow \frac{\mathrm{x}-\mathrm{x}_1}{\mathrm{x}_2-\mathrm{x}_1}=\frac{\mathrm{y}-\mathrm{y}_1}{\mathrm{y}_2-\mathrm{y}_1}=\frac{\mathrm{z}-\mathrm{z}_1}{\mathrm{z}_2-\mathrm{z}_1}$$\begin{aligned} & \text{ i.e, } \frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+1}{3}=K(\text{ say }) \\ & \Rightarrow x-1=2 K ; y-2=-3 K ; z+1=3 K \\ & \Rightarrow x=2 K+1 ; y=-3 K+2 ; z=3 K-1 \end{aligned}$Since the line meets $y z$ plane, $x=0\begin{aligned} & \therefore 2 \mathrm{ K}+1=0 \Rightarrow \mathrm{ K}=\frac{-1}{2} \\ & \therefore \mathrm{y}=-3\left(\frac{-1}{2}\right)+2=\frac{3}{2}+2=\frac{7}{2} \\ & \mathrm{z}=3\left(\frac{-1}{2}\right)-1=\frac{-3}{2}-1=\frac{-5}{2} \end{aligned}$$$