Statement 1: A plane passes through the point `A(2,1,-3)dot` If distance of this plane from origin is maximum, then its equation is `2x+y-3z=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 adot`

Options

A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true.

Answer

b

Explanation

The direction cosines of segment OA are
`" "(2)/(sqrt(14)), (1)/(sqrt(14)) and (-3)/(sqrt(14))`.
`" "OA= sqrt(14)`
This means `OA` will be normal to the plane and the equation of the plane is `2x+y-3z=14`.