Plane x+y+z= a cuts the unit cube with one vertex at origin and three adjacent vertices at positive x, y, z axes.

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for a∈(1,2) the area of intersection is a hexagon with angles θ1,θ2,……,θ6 such that cos⁡θ1+cos⁡θ2….+cos⁡θ6=−3.

For a=32 area enclosed by the intersection is 334

For a=43 area enclosed by the intersection is 13318

Maximum area of intersection is when a=1 or 2.

answer is A.

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Detailed Solution

The figure formed is a hexagon with all interior angles as 120∘(a∈(1,2)).

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