Analytic Geometry 3D Mock Tests

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

Let P = (1, 0, 1) and Q = (3, 2, -1). Let S be the set of all points X in ℝ³ such that dist(X, P)² - dist(X, Q)² = 20. Which of the following statements is/are TRUE?

The shortest distance between the lines L1: x = t, y = 1, z = 2 and L2: x = 1, y = s, z = 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

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

The shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-4)/4 = (z-5)/5 is equal to:

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