3D Geometry
Shortest Distance Between Diagonal and Edge
nta_pyq_2023_apr
Grade 12
Question:
One vertex of a rectangular parallelopiped is at origin $O$; edges along axes are 3, 4, 5. $P=(3,4,5)$. Shortest distance between diagonal $OP$ and an edge parallel to $z$-axis (not through $O$ or $P$) is
\dfrac{12}{\sqrt{5}}
12\sqrt{5}
\dfrac{12}{5\sqrt{5}}
\dfrac{12}{5}
Step-by-Step Solution
Key Concept: Direction of $OP$: $(3,4,5)$. The edge parallel to $z$-axis through $(3,4,0)$: direction $(0,0,1)$. Use SD formula.
SD $=\frac{12}{5}$.
Correct Answer: 4