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Statement 1: A plane passes through the point $A (2, 1, - 3)$ . If distance of this plane from origin is maximum, then its equation is $2 x + y - 3 z = 14$ .
Statement 2: If the plane passing through the point $A (\vec{a})$ is at maximum distance from origin, then normal to the plane is vector $\vec{a}$ .

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Both the statements are true, and Statement 2 is the correct explanation for Statement1.

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

Statement 1 is true and Statement 2 is false.

Statement 1 is false and Statement 2 is true.

answer is A.

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Detailed Solution

The direction cosines of segment OA are
$\frac{2}{\sqrt{14}}, \frac{1}{\sqrt{14}} and \frac{- 3}{\sqrt{14}} .$
$O A = \sqrt{14} n$
This means OA will be normal to the plane and the equation of the plane is $2 x + y - 3 z = 14$

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