3D Geometry
Perpendicular Lines — Finding 4λ+9μ
nta_pyq_2024_apr
Grade 12
Question:
If the line $\dfrac{2-x}{3}=\dfrac{3y-2}{4\lambda+1}=4-z$ makes a right angle with the line $\dfrac{x+3}{3\mu}=\dfrac{1-2y}{6}=\dfrac{5-z}{7}$, then $4\lambda+9\mu$ is equal to:
Step-by-Step Solution
Key Concept: Rewrite DRs: Line 1 has DRs $(-3,(4\lambda+1)/3,-1)$. Line 2 has DRs $(3\mu,-3,-7)$. For perpendicularity, dot product $=0$.
Perpendicularity condition gives $4\lambda+9\mu=6$.
Correct Answer: 4