Let `P\ a n d\ Q` be any two points. Find the coordinates of the point `R\ ` which divides `P Q` externally in the ratio 2:1 and verify that `Q` is the mid point of `P R` .

Find the coordinates of the point R which divides the join of P(0,0,0) and Q(4,-1,-2) in the ratio 1:2 externally and verify that P is the mid point of RQ.

Find the coordinates of points P ,\ Q ,\ R\ a n d\ S in Figure.

The coordinates of the point P are (-3,\ 2) . Find the coordinates of the point Q which lies on the line joining P and origin such that O P=O Q .

If point P(3,2) divides the line segment AB internally in the ratio of 3:2 and point Q(-2,3) divides AB externally in the ratio 4:3 then find the coordinates of points A and B.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2\ vec a+ vec b) and ( vec a-\ 3 vec b) respectively, externally in the ratio 1:2.Also, show that P is the mid-point of the line segment R Qdot

Consider two points P and Q with position vectors -> O P=3 -> a-2 -> b and -> O Q= -> a+ -> b Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.

M is the mid-point of the line segment joining the points A(-3, 7) and B(9, -1). Find the co-ordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q.

If P is the point (1,0) and Q is any point on the parabola y^(2) = 8x then the locus of mid - point of PQ is

A point R with x-coordinates 4 lies on the line segment joining the points P(2,-3,4)a n d\ Q(8,0, 10)dot Find the coordinates of the point Rdot

Let P and Q be two points on the circle |w|=r represented by w_1 and w_2 respectively, then the complex number representing the point of intersection of the tangents of P and Q is :