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.

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) .

Let C be the midpoint of the line-segment joining the points A and B , if vec(a) " and " vec(c) are the position vectors of the points A and C respetively, then the position vector of the vector of the point B will be -

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) .

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

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.

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 -

(i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

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

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 vectors of two given points P and Q are 8hat(i)+3hat(j) " and " 2hat(i)-5hat(j) respectively, find the magnitude and direction of the vector vec(PQ)