P(-2, -3, 5), Q(4, -1, 5), R(6, -4, 8), and S(2, -6, 10) are four points in 3D space. Consider the following statements: I. PQ is parallel to RS. II. PR is perpendicular to QS. Which of the statements given above is/are correct?

If θ is the acute angle between the planes x + 2y + 2z = 0 and 2x - 2y + z = 0, then cos(θ) is equal to:

Find the vector equation for the line passing through the points A(2, 1, 5) and B(4, 5, 7).

Find the angle between the pair of lines given by: r = î - 2ȷ - 4k̂ + λ(-2î + 2ȷ + k̂) and r = 4î + ȷ - 3k̂ + μ(2î - 4ȷ - 3k̂).