Let L be the line x + 12 = y + 13 = z + 36 and let S be the set of all points (a, b, c) on L, whose distance from the line x + 12 = y + 13 = z - 90 along the line L is 7. Then Σ(a,b,c)∈S(a + b + c) is equal to:

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).