The position vectors of the points A and B are `2 veca + vecb` and `veca - 3vecb`. If the point C divides the line segment `bar (AB)` externally in the ratio `1:2`, then find the position vector of the point C. Show also that A is the midpoint of the line segment `bar (CB)`.

The position vectors of the points A and B are 2vec(a)+vec(b) " and " vec(a)-3vec(b) . If the point C divides the line-segment bar(AB) externally in the ratio 1:2, then find the position vector of the point C. Show also that A is the midpoint of the line-segment bar(CB) .

The position vector of a point A is veca+2vecb and veca divides AB internally in the ratio 2:3 , then the position vector of the point B is -

If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the position vectors of the points A and B respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vectors of the points of trisection of the line-segment bar(AB) .

The position vecors of the points A and B are 4hat(i)-3hat(j)+5hat(k) " and " -2hat(i)+3hat(j)+2hat(k) respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vector of the points of trisection of the line-segment bar(AB) .

Point R (h, k) divides a line segment between the axes in the ratio 1:2 Find equation of the line.

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.

A point divides the line -segment joining the points (2,-5) and (-3,-2) externally in the ratio 4:3 . State which of the follwing is the ordinate of the point ?

A(2,5) and B(-3,-4) are two fixed points , the point P divides the line -segment overline(AB) internally in the ratio k:1 . Find the coordinates of P . Hence find the equation of the line joining A and B.

A point divides the line segment joining the point (2, -5. 8) and(3, 4. -6) internally in the ratio 3 : 5. Find the .co-ordinate of that point.

If any points divides the line segment joining the points (2, -5) and (-3, -2) into the ratio 4 : 3 externally. Then the ordinate of the point is