A point Q at a distance 3 from the point `P(1, 1, 1)` lying on the line joining the points
`A(0, -1, 3)` and P has the coordinates

If the point (p,q) lies on the line joining the points (-4,5) and (-5,7) , then show that 2p+q+3=0 .

If the distance from the point P(1, 1, 1) to the line passing through the points Q(0, 6, 8) andR(-1, 4, 7) is expressed in the form sqrt((p)/(q)) , where p and q are co-prime, then the value of ((q+p)(p+q-1))/(2) is equal to

Find the distance of the point P(–1, –5, –10) from the point of intersection of the line joining the points A(2, –1, 2) and B(5, 3, 4) with the plane x – y + z = 5.

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

The projection of the line segment joining the points (1, -1, 3) and (2, -4, 11) on the line joining the points (-1, 2, 3) and (3, -2, 10) , is ……

Find the equation of the perpendicular dropped from the point (-1, 2) onto the line joining the points (1, 4) and (2, 3).

A point with x-coordinate 9 lies on the line segment joining the points (8, 1, 1) and (10, -2, -3). Find the coordinates of the point.

A point R with x - coordinate 4 lies on the line segment joining the points P(2,-3,4) and Q(8, 0, 10) . The coordinates of R are

Find the distance of the point P(-1,-5,-10) from the point of intersection of the line joining the points A(2,-1,2)a n dB(5,3,4) with the plane x-y+z=5.

Find the coordinates of the foot of perpendicular drawn from th point A(1,8,4) to the line joining the points B(0,-1,3)a n dC(2-3,-1)dot