Analytic Geometry 3D Mock Tests

Let L be the line passing through points (1, 2, 3) and (4, 5, 6). The shortest distance from the point (1, 1, 1) to the line L is:

Let S be the set of all points X in R^3 such that the distance from X to the point P(0, 0, 0) is twice the distance from X to the point Q(6, 0, 0). The set S is

The angle between the lines (x-1)/1 = (y-2)/1 = (z-3)/0 and (x-2)/1 = (y-3)/(-1) = (z-4)/1 is:

Let S be the set of all points X(x,y,z) in R^3 such that |X - (0,0,0)|^2 - |X - (3,0,0)|^2 = 9. The set S is

The shortest distance between the lines x/1 = (y-1)/0 = (z-2)/0 and (x-1)/0 = y/1 = (z-1)/0 is

The shortest distance between the parallel lines x/1 = (y-1)/0 = (z-0)/0 and (x-1)/1 = (y-0)/0 = (z-1)/0 is

The locus of a point P in space such that the sum of its distances from the points A(1,0,0) and B(-1,0,0) is equal to 4 is

Let P = (1, 2, 3) and Q = (4, 0, −1) be two fixed points in ℝ³. Let S be the set of all points X = (x, y, z) such that dist(X, P)² − dist(X, Q)² = 50. Which of the following statements is/are TRUE?