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JEE 2023 Mathematics PYQ — One vertex of a rectangular parallelepiped is at the origin O and… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units respectively. Let P be the vertex (3, 4, 5). Then the shortest distance between the diagonal OP and an edge parallel to z axis, not passing through O or P is :

Choose the correct answer:

A.
$\frac{12}{5 5}$

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Let two vertices of a triangle $A B C$ be $(2, 4, 6)$ and $(…

B.
$125$

C.
$\frac{12}{5}$
(Correct Answer)

D.
$\frac{12}{5}$

Correct Answer:
$\frac{12}{5}$

Explanation

Equation of OP is $\frac{x}{3} = \frac{y}{4} = \frac{z}{5}$
$a_{1} = (0, 0, 0), a_{2} = (3, 0, 5), b_{1} = (3, 4, 5), b_{2} = (0, 0, 1)$
Equation of edge parallel to z axis $\frac{x - 3}{0} = \frac{y - 0}{0} = \frac{z - 5}{1}$
Shortest distance $= \frac{3 \times 4}{∣4 i ^ - 3 j ^ ∣} = \frac{12}{5}$

Explanation

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