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 :

The shortest distance between the lines

$${{x - 1} \over 0} = {{y + 1} \over { - 1}} = {z \over 1}$$

and x + y + z + 1 = 0, 2x – y + z + 3 = 0 is :

If for some $$\alpha $$ $$ \in $$ R, the lines

L₁ : $${{x + 1} \over 2} = {{y - 2} \over { - 1}} = {{z - 1} \over 1}$$ and

L₂ : $${{x + 2} \over \alpha } = {{y + 1} \over {5 - \alpha }} = {{z + 1} \over 1}$$ are coplanar,

then the line L₂ passes through the point :

If (a, b, c) is the image of the point (1, 2, -3) in

the line $${{x + 1} \over 2} = {{y - 3} \over { - 2}} = {z \over { - 1}}$$, then a + b + c is :