What is the angle between the two lines having direction ratios (6, 3, 6) and (3, 3, 0)?

If l, m, n are the direction cosines of the line x - 1 = 2(y + 3) = 1 - z, then what is l⁴ + m⁴ + n⁴ equal to?

What is the number of possible values of k for which the line joining the points (k, 1, 3) and (1, -2, k + 1) also passes through the point (15, 2, -4)?

The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is