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 co-ordinates of the point which divided the join of P(5,-2) and Q(9,6). externally in ratio 3:1

Find the co-ordinates of the point which divided the join of P(5,-2) and Q(9,6). internally in ratio 3:1

Find the coordinates of the point which divides the join of the points. P (5,4,2) & Q(-1,-2,4) in the ratio 2:3

Let O be the vertex and Q be any point on the parabola x^2=8y . IF the point P divides the line segment OQ internally in the ratio 1:3 , then the locus of P is

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments OQ internally in the ratio 1 : 3 , then the locus of P is _

If P and Q are any two set then P-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 (2veca+vecb)and(veca-3vecb) externally in the ratio 1:2 Also , show that P is the mid point of the line segment RQ.

Let vec(a) " and " vec(b) be the position vectors of two given points P and Q respectively. To find the position vector of the point R which divides the line segment bar(PQ) internally in the ratio m:n.

Consider two points P and Q with position vectors vec(OP)=3veca-2vecbandvec(OQ)=veca+vecb . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 , (i) intermally , and (ii) externally.