Find the condition that the points (x,y) may lie on the line joining (3,4) and (-5,-6).

Find image of the point (1,0,3) to the line joining points (4,7,1) and (3,5,3) .

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 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).

If each of the points (x_1,4),(-2,y_1) lies on the line joining the points (2,-1)a n d(5,-3) , then the point P(x_1,y_1) lies on the line.

Find the length of the projection of the line segment joining (3,4,5) and (4,6,3) on the straight line : (x-4)/2=(y-5)/3=(z-6)/6

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

Find the angle between the x-axis and the line joining the points (3,-1) and (4,-2).

Find the ratio in which the plane 3x+ 4y-5z =1 divides the line joining the points (-2, 4, -6) and (3, - 5, 8).

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.