Introduction to 3-Dimensional Geometry

Find the ratio in which the line segment joining the points A (1, 4, 6) and B ( - 4, - 3, 5) is divided by YZ-plane.

Three vertices of a parallelogram ABCD are A (3,4,6), B (-1,0,6) and C (5,2,0). Find the coordinates of D.

Find the ratio in which the line segment joining the points A (1,2,3) and B (-4,5,-2) is divided by the plane x + 2y - z = 4.

Show that the points (3,2,2), (-1,1,3), (0,5,6) and (2,1,2) lie on a sphere whose centre is (1,3,4). Find the radius of sphere.

Given that P (3,2,-4), Q (5,4,-6) and R (9,8,-10) are collinear. Find the ratio in which Q divides the join of P and R.

Find the distance between the points. P (-2,4,1) and Q (1,2,-5).