One vertex of a rectangular parallelopiped is at the origin … and the lengths of its edges along … and … axes are … and … units respectively. Let … be the vertex …. Then the shortest distance between the diagonal OP and an edge parallel to … axis, not passing through … or … is :

3d Geometry

JEE Main 2023 · 6 Apr, Morning shift · Q2520

MathematicsHard249×since 2002Q2520

One vertex of a rectangular parallelopiped is at the origin

\mathrm{O}

and the lengths of its edges along

x, y

and

z

axes are

3,4

and

5

units respectively. Let

\mathrm{P}

be the vertex

(3,4,5)

. Then the shortest distance between the diagonal OP and an edge parallel to

\mathrm{z}

axis, not passing through

\mathrm{O}

\mathrm{P}

is :