If the position vector of a point A is `vec a + 2 vec b and vec a ` divides AB in the ratio `2:3`, then the position vector of B, is

If a and b are position vector of two points A,B and C divides AB in ratio 2:1, then position vector of C is

A and B are two points. The position vector of A is 6b-2a. A point P divides the line AB in the ratio 1:2. if a-b is the position vector of P, then the position vector of B is given by

The position vector of the point which divides the join of points 2 vec a -3 vec b and vec a+vec b in the ratio 3: 1 is

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

If |vec a|=10, and |vec b|=2 and vec a* vec b =12 , find angle between the two vectors

If A,B,C,D are the points with position vectors vec a , vec b , 3 vec a+ 2 vec b and vec a- 2 vec b respectively , show that vec AC = 2 vec a + 2 vec b and vec DB= 3 vec b - a .

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

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

Statement 1: if three points P ,Qa n dR have position vectors vec a , vec b ,a n d vec c , respectively, and 2 vec a+3 vec b-5 vec c=0, then the points P ,Q ,a n dR must be collinear. Statement 2: If for three points A ,B ,a n dC , vec A B=lambda vec A C , then points A ,B ,a n dC must be collinear.

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.