Let the plane P : 4x - y + z = 10 be rotated by an angle π/2 about its line of intersection with the plane x + y - z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α 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).