Let the system of linear equations: -x + 2y - 9z = 7 -x + 3y + 7z = 9 -2x + y + 5z = 8 -3x + y + 13z = λ has a unique solution x = α, y = β, z = γ. Then the distance of the point (α, β, γ) from the plane 2x - 2y + z = λ is:

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).