Three Dimension...

The foot of the perpendicular from (2, 4, -1) to the line x + 5 = 1/4 (y + 3) = 1/9 (z - 6) is

A line with direction ratios proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The coordinates of each of the points of intersection are given by

The equation of the straight line passing through the points (4, -5, -2) and (-1, 5, 3)

If the points (1, 2, 3) and (2, -1, 0) lie on the opposite sides of the plane 2x + 3y - 2z = k, then

The volume of the tetrahedron included between the plane 3x + 4y - 5z - 60 = 0 are coordinate plane is

If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is

The equation of the plane through the intersection of the plane 3x - y + 2z - 4 = 0, x + y + z - 2 = 0 and the point (2, 2, 1) is