What is the acute angle between the pair of straight lines $$\sqrt 2 x + \sqrt 3 y = 1$$ and $$\sqrt 3 x + \sqrt 2 y = 2$$ ?

If the centroid of a triangle formed by (7, x), (y, $$-$$6) and (9, 10) is (6, 3), then the values of x and y are respectively

The angle between the two lines $$lx + my + n = 0$$ and $$l'x + m'y + n' = 0$$ is given by $${\tan ^{ - 1}}\theta $$. What is $$\theta$$ equal to?

Consider the following statements

1. The distance between the lines $$y = mx + {c_1}$$ and $$y = mx + {c_2}$$ is $${{\left| {{c_1} - {c_2}} \right|} \over {\sqrt {1 + {m^2}} }}$$.

2. The distance between the lines $$ax + by + {c_1} = 0$$ and $$ax + by + {c_2} = 0$$ is $${{\left| {{c_1} - {c_2}} \right|} \over {\sqrt {{a^2} + {b^2}} }}$$.

3.The distance between the lines $$x = {c_1}$$ and $$x = {c_2}$$ is $$\left| {{c_1} - {c_2}} \right|$$.

Which of the above statements are correct?