The vector equation of the plane passing through the intersection

of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {\widehat i - 2\widehat j} \right) = - 2$$, and the point (1, 0, 2) is :

The equation of the plane passing through the point (1, 2, -3) and perpendicular to the planes

3x + y - 2z = 5 and 2x - 5y - z = 7, is :

The distance of the point (1, 1, 9) from the point of intersection of the line $${{x - 3} \over 1} = {{y - 4} \over 2} = {{z - 5} \over 2}$$ and the plane x + y + z = 17 is :

A plane P meets the coordinate axes at A, B and C respectively. The centroid of $$\Delta $$ABC is given to be (1, 1, 2). Then the equation of the line through this centroid and perpendicular to the plane P is :