3D Geometry
Shortest distance between a segment and a line
nta_pyq_2023_jan
Grade 12
Question:
If the shortest distance between the line joining the points $(1, 2, 3)$ and $(2, 3, 4)$, and the line $\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-2}{0}$ is $\alpha$, then $28\alpha^2$ is equal to _____.
Step-by-Step Solution
Key Concept: Apply the skew lines shortest distance formula with $\vec{b_1} = (1,1,1)$ and $\vec{b_2} = (2,-1,0)$.
$\alpha = 3/\sqrt{14}$, $28\alpha^2 = 28 \cdot 9/14 = 18$. Answer: 18
Correct Answer: 18