A plane passes through the point A(2, 1, -3). Among all such planes, the one for which the distance from the origin is maximum has the equation:

2x + y - 3z = 14
2x + y + 3z = 2
x + y - z = 1
None of these

Correct answer: 2x + y - 3z = 14

Solution

For the distance from the origin to a plane passing through a fixed point to be maximum, the plane must be perpendicular to OA. The normal direction is (2, 1, -3). The plane equation is 2(x-2) + 1(y-1) - 3(z+3) = 0, which gives 2x + y - 3z = 14.

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