A rectangle ABCD of dimensions r and 2r is folded along the diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remain unchanged and C 1 is the

Question

A rectangle ABCD of dimensions r and 2r is folded along the diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remain unchanged and C 1 ​ is the new position of C. The shortest distance between the edges AB and C 1 ​ D is equal to

TestHub · Accepted Answer

Any point on AB: ( 0 , 0 , 0 ) , direction cosines of AB: 0, 1, 0. Any point on C 1 ​ D : ( r , 2 r , 0 ) , direction cosines of C 1 ​ D : 5 2 ​ , 5 4 ​ , − 5 ​ 1 ​ . Shortest distance = ( 5 ​ 1 ​ ) 2 + ( 5 2 ​ ) 2 ​ ​ r ​ 2 r ​ 00 ​ 1 ​ 0 5 2 ​ ​ 5 4 ​ ​ − 5 ​ 1 ​ ​ ​ ​ = 5 3 ​ 5 ​ r ​ ​ = 3 5 ​ r ​ unit.

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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