3D Geometry
Shortest distance between skew lines
nta_pyq_2023_jan
Grade 12
Question:
Shortest distance between the lines $\frac{x-1}{2} = \frac{y+8}{-7} = \frac{z-4}{5}$ and $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-6}{-3}$ is
$2\sqrt{3}$
$4\sqrt{3}$
$3\sqrt{3}$
$5\sqrt{3}$
Step-by-Step Solution
Key Concept: Use the skew lines SD formula. $\vec{p}\times\vec{q} = 16(\hat{i}+\hat{j}+\hat{k})$.
$SD = \frac{|(-10j-2k)\cdot 16(\hat{i}+\hat{j}+\hat{k})|}{16\sqrt{3}} = \frac{|-160-32|}{16\sqrt{3}} = \frac{12}{\sqrt{3}} = 4\sqrt{3}$. Answer: (2)
Correct Answer: $4\sqrt{3}$