Verified Solution • 2025–26 Session moderate

QJEEM24Ma9655: JEE Main 2024 Mathematics - Class 12 JEEM24Ma9655 Solution: If the line makes a right angle with the line , then is equal…

If the line 2−x3=3y−24λ+1=4−z\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z makes a right angle with the line x+33μ=1−2y6=5−z7\frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7} , then 4λ+9μ4 \lambda+9 \mu is equal to :

Multiple Choice Options

  • A 4
  • B 13
  • C 5
  • D 6

Step-by-Step Verified Solution

amp;L1:x−2(−3)=y−23(4λ+13)=(−1)amp;L2:x+33μ=y−12−3=z−5−7amp;∵L1⊥L2amp;⇒(−3)(3μ)+(4λ+13)(−3)+(−1)(−7)=0amp;−9μ−4λ−1+7=0amp;⇒4λ+9μ=6amp;\begin{aligned}& L_1: \frac{x-2}{(-3)}=\frac{y-\frac{2}{3}}{\left(\frac{4 \lambda+1}{3}\right)}=\frac{}{(-1)} \\& L_2: \frac{x+3}{3 \mu}=\frac{y-\frac{1}{2}}{-3}=\frac{z-5}{-7} \\& \because L_1 \perp L_2 \\& \Rightarrow(-3)(3 \mu)+\left(\frac{4 \lambda+1}{3}\right)(-3)+(-1)(-7)=0 \\& -9 \mu-4 \lambda-1+7=0 \\& \Rightarrow 4 \lambda+9 \mu=6 \\&\end{aligned}

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