Find the position vectors of the points which divide the join of the points `2 vec a-3 vec ba n d3 vec a-2 vec b` internally and externally in the ratio `2:3` .

Find the position vector of a point which divides the join of points with position vectors vec a-2 vec b and 2 vec a+ vec b externally in the ratio 2:1.

The position vector of the point which divides the line segment joining the points with position vectors 2 vec(a) = 3b and vec(a) + vec(b) in the ratio 3:1 is

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

If the position vector of a point (-4,-3) be vec a , find |a| .

P ,Q have position vectors vec a& vec b relative to the origin ' O^(prime)&X , Ya n d vec P Q internally and externally respectgively in the ratio 2:1 Vector vec X Y= 3/2( vec b- vec a) b. 4/3( vec a- vec b) c. 5/6( vec b- vec a) d. 4/3( vec b- vec a)

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

If vec a , vec b are the position vectors of the points (1,-1),(-2,m), find the value of m for which vec a and vec b are collinear.

A, B have vectors vec a , vec b relative to the origin O and X, Y divide vec(AB) internally and externally respectively in the ratio 2:1 . Then , vec (XY)=

If vec a ,vec b,vec c and vec d are the position vectors of the points A, B, C and D respectively in three dimensionalspace no three of A, B, C, D are collinear and satisfy the relation 3vec a-2vec b +vec c-2vec d = 0 , then

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec a- vec d , then show that A B C D is parallelogram.