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A square ABCD of diagonal length 2a, is ...

A square ABCD of diagonal length 2a, is folded along the diagonal AC so that the planes DAC, BAC are at right angles. The shortest distance between DC and AB is

A

`sqrt(2)a`

B

`2a//sqrt(3)`

C

`2a//sqrt(5)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
C
Let
`f(x)=x("ln" x-1)`
`f(x) = "ln"x`
`f''(x)=(1)/(x)" "," "underset(1)overset(e)(int)((f''+f)sinx)dx`
Use integration by parts =`intf''.sinx+intf.sinx`
`=sinx.f']_(1)^(e)-intcosx.f'+f.(-cosx)]_(1)^(e)-intf'.(-cosx)=sinx. "ln"x]_(1)^(e)-x("ln"x-1).(cosx)]_(1)^(e)`
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