`veca, vecb, vecc` are the position vectors of the three points A,B,C respectiveluy. The point P divides the ilne segment AB internally in the ratio 2:1 and the point Q divides the lines segment BC externally in the ratio 3:2 show that `3vec(PQ) = -veca-8vecb+9vecc`.

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.

If veca,vecb,vecc,vecd be the position vectors of points A,B,C,D respectively and vecb-veca=2(vecd-vecc) show that the pointf intersection of the straighat lines AD and BC divides these line segments in the ratio 2:1.

The point which divides the line segment joining the points (8,–9) and (2,3) in ratio 1 : 2 internally lies in the

Find the position vector of the points which divide the join of the points 5veca-4vecb and 4veca-5vecb internally and externally in the ratio 4:3 respectively.

P and Q are two points with position vectors 3 vec a-2 vec b and vec a+ vec b respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

The position vector of the point which divides the join of points 2veca-3vecbandveca+vecb in the ratio 3:1, is

If veca,vecb,vecc & vecd are position vector of point A,B,C and D respectively in 3-D space no three of A,B,C,D are colinear and satisfy the relation 3veca-2vecb+vecc-2vecd=0 then (a) A, B, C and D are coplanar (b) The line joining the points B and D divides the line joining the point A and C in the ratio of 2:1 (c) The line joining the points A and C divides the line joining the points B and D in the ratio of 1:1 (d)The four vectors veca, vecb, vec c and vecd are linearly dependent .

If veca, vecb, vecc, vecd are the position vectors of points A, B, C and D , respectively referred to the same origin O such that no three of these points are collinear and veca+vecc=vecb+vecd , then prove that quadrilateral ABCD is a parallelogram.

Find the position vector of the point which divides the join of the points (2veca - 3vecb) and (3veca - 2vecb) (i) internally and (ii) externally in the ratio 2 : 3 .

If O be the origin the vector vec(OP) is called the position vector of point P. Also vec(AB)=vec(OB)-vec(OA) . Three points are said to be collinear if they lie on the same stasighat line.Points A,B,C are collinear if one of them divides the line segment joining the others two in some ratio. Also points A,B,C are collinear if and only if vec(AB)xxvec(AC)=vec0 Let the points A,B, and C having position vectors veca,vecb and vecc be collinear Now answer the following queston: (A) veca.vecb=veca.vecc (B) vecaxxvecb=vecc (C) vecaxxvecb+vecbxxvecc+veccxxveca=vec0 (D) none of these