3D Geometry
Shortest distance between skew lines
nta_pyq_2023_jan
Grade 12
Question:
If the shortest distance between the lines $\frac{x+\sqrt{6}}{2} = \frac{y-\sqrt{6}}{3} = \frac{z-\sqrt{6}}{4}$ and $\frac{x-\lambda}{3} = \frac{y-2\sqrt{6}}{4} = \frac{z+2\sqrt{6}}{5}$ is 6, then the square of sum of all possible values of $\lambda$ is
Step-by-Step Solution
Key Concept: Find the vector along the common perpendicular (cross product of direction vectors), set up SD formula equal to 6 and solve for $\lambda$.
SD formula gives $\lambda = -2\sqrt{6}$ or $10\sqrt{6}$. Sum $= 8\sqrt{6}$. Square of sum $= 384$. Answer: 384
Correct Answer: 384