Show that the line segments joining the points (1,-2),(1,2) and (3,0),(-1,0) bisect each other.

Show that the line segments joining the points (4, 7, 8), (-1, -2, 1) and (2, 3, 4), (1, 2, 5) intersect. Verify whether the four points concyclic.

Find the equation of the line joining the points A(0,-1,3) and B(2,-3,-1).

Find the length of the projection of the line segment joining the points P(3,-1,2) and Q(2,4-1) on the line with direction ratios

The line segment joining the points (-3,-4) and (1,-2) is divided by y-axis in the ratio:

Find the co-ordinates of the point which divides the line segment joining the points (-2,3,5) and (1,-4,6) in the ratio. 2 : 3 Internally

Find the co-ordinates of the point which divides the line segment joining the points (-2,3,5) and (1,-4,6) in the ratio. 2 : 3 externally.

Find the length of the projection of the line segment joining the point A(-1,2,0) and B(1,-1,2) on the plane 2x-y-2z-4=0 .

What is the position vector of the mid-point of the line segment joining the points A(2,3,4) and B(4,1,-2).

Find the coordinates of the point which divides the line segment joining the points A(5,-2) and B(9,6) in the ratio 3:1

Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1,-4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.