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A B C D is a square whose vertices are A...

`A B C D` is a square whose vertices are `A(0,0),B(2,0),C(2,2),` and `D(0,2)` . The square is rotated in the `X Y-p l a n e` through an angle `30^0` in the anticlockwise sense about an axis passing though `A` perpendicular to the `X Y-p l a n e` . Find the equation of the diagonal `B D` of this rotated square.

Text Solution

Verified by Experts

We have
`"B" -= (2cos 30^(@), 2sin 30^(@)) = (sqrt(3),1)`
`"D" -= (-2 sin 30^(@), 2 cos 30^(@)) = (-1, sqrt(3))`
Hence, the equation of BD is

`y-1 = (sqrt(3)-1)/(-(sqrt(3) + 1))(x-sqrt(3))`
`=(sqrt(3)-2)(x-sqrt(3))`
i.e., `(2-sqrt(3))x+y = 2sqrt(3) - 2`
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