The x, co-ordinate of a point on the line joining the points Q (2, 2, 1) and R (5, 1, - 2) is 4. Find its z-co-ordinate

A point R with x-co-ordinate 4 lies on the line segment joining the points P(2,-3,4) and Q(8,0,10). Find the co-ordinate of the point R.

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

Find the co-ordinates of the mid-point of the join of the points A (3, 5, 7) and B(-3,-3, 1).

Find the distance of the point (1,2,3) from the line joining the points (-1,2,5) and (2,3,4).

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 co-ordinates of the point where the line joining the points (1,-2,3) and (2,-1,5) cuts the plane x-2y+3z=19 . Hence, find the distance of this point from the point (5,4,1).

P is a point on the line segment joining the points (3, 2, -1) and (6, 2,-2). If x co-ordinates of P is 5, then its y co-ordinate is

P is a point on the line joining A (4, 3) and B (- 2, 6) such that (AP)/(BP)=2/5 . Find the co-ordinates of P.