Consider the following statements:

1. A-line in space can have infinitely many direction ratios.

2. It is possible for certain lines that the sum of the squares of direction cosines can be equal to the sum of its direction cosines.

Which of the above statements is/are correct?

The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)

The number of spheres of radius r touching the coordinate axes is

ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α is the angle between AB and AG; β is the angle between AC and AG, then what is the value of cos 2α + cos 2β?