Find a point on the line thorugh A(-5,-4) and B(2,3) that is twice as far from A as from B.

Find the points on the line through the points A(1,2,3) and B(5,8, 15) at a distance of 14 units from the mid point of AB.

The co-ordinates of two points A and B are (-1, 4) and (5, 1) respectively. Find the co-ordinates of the point P, which lies on extended time AB such that it is three times as far from B as from A.

Find the equation of the locus of the points twice as from (-a, 0) as from (a, 0).

Find the direction cosines of the vector joining the points A(1,2,-3) and B(-1,-2,1) , directed from A to B.

Find the direction cosines of the vector joining the points A(1,2,-3) and B(-1,-2,1) directed from A to B.

Find the points on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance of 5 units from the point (1,3,3).

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.

Prove that the line through A(0,-1,-1) and B(4,5,1) intersects the line through C(3,9,4) and D(-4,4,4). Also find their point of intersection.

Find the direction cosines of the vector joining the points A(1, 2, 3) and B(1, 2, 1) , directed from A to B.