If for a > 0, the feet of perpendiculars from the points A(a, $$-$$2a, 3) and B(0, 4, 5) on the plane lx + my + nz = 0 are points C(0, $$-$$a, $$-$$1) and D respectively, then the length of line segment CD is equal to :

If the mirror image of the point (1, 3, 5) with respect to the plane

4x $$-$$ 5y + 2z = 8 is ($$\alpha$$, $$\beta$$, $$\gamma$$), then 5($$\alpha$$ + $$\beta$$ + $$\gamma$$) equals :

Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and y + 2z = 4. If point P($$\alpha$$, $$\beta$$, $$\gamma$$) is the foot of perpendicular from (3, 2, 1) on L, then the
value of 21($$\alpha$$ + $$\beta$$ + $$\gamma$$) equals :

Consider the three planes

P₁ : 3x + 15y + 21z = 9,

P₂ : x $$-$$ 3y $$-$$ z = 5, and

P₃ : 2x + 10y + 14z = 5

Then, which one of the following is true?