If A and B are the positon vectors of `bar(a)` and `bar(b)` respectively, then find the positon vector of a point C in `vec(BA)` produced such that `vec(BC)=1.5vec(BA)`.

The position vector of the points A and B are respectively vec(a) and vec(b) . Find the position vectors of the points which divide AB in trisection.

Consider two points P and Q with position vectors 2vec(a)+vec(b) and vec(a)-3vec(b) respectively. Find the position vector of a point R which divide the line segment joining P and Q in the ratio. 1 : 2 externally. Prove that P is a midpoint of line segment RQ.

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 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 quadrilateral A B C D is a ;

The position vectors of the points A, B, C are vec(a),vec(b) and vec( c ) respectively. If the points A, B, C are collinear then prove that vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xxvec(a)=vec(0) .

Consider two points P and Q with position vectors vec(OP)=3hata-2vec(b) and vec(OQ)=vec(a)+vec(b) . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (i) internally, and (ii) 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 aa n d vec b are collinear.

Vectors drawn from the origin O to the points A , B and C are respectively vec a , vec b and 4veca- 3vecbdot find vec(AC) and vec(BC)dot

If theta is angle between two vectors vec(a) and vec(b) then vec(a).vec(b)ge 0 only when …….