If the line $\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z$ makes a right angle with the line $\frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7}$, then $4 \lambda+9 \mu$ is equal to :

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Aicharya · Accepted Answer

$\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z...(1)$ $\frac{x-2}{(-3)}=\frac{y-\frac{2}{3}}{\left(\frac{4 \lambda+1}{3}ight)}=\frac{z-4}{(-1)}$ $\begin{aligned} & \frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7}...(2) \ & \frac{x+3}{3 \mu}=\frac{y-\frac{1}{2}}{(-3)}=\frac{z-5}{(-7)} \ & 	ext { Right angle } \Rightarrow(-3)(3 \mu)+\left(\frac{4 \lambda+1}{3}ight)(-3)+(-1)(-7)=0 \ & -9 \mu-4 \lambda-1+7=0 \ & 4 \lambda+9 \mu=6\end{aligned}$

If the line $\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z$ makes a right angle with the line $\frac{x+3}{3…

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