The position vector of two points A and B are `6veca+2vecb` and `veca-3vecb.` If point C divides AB in the ratio 3:2 then show that the position vector of C is `3veca-vecb`

The position vectors of two points A and B are 3veca+2vecb and 2veca-vecb respectively. Find the vector vec(AB)

The position vectors of the points A and B are veca and vecb respectively. P divided [AB] in the ratio 3:1, Q is mid-point of [AP]. The positin vector of Q is :

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) .

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 -

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

Let veca,vecb be the position vectors of points A and B with respect to and |veca|=a,|vecb|=b . The points Cand D divide AB internally and externally in the ratio 2: 3 respectively. If vec(OC)andvec(OD) are perpendicular, then

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

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

The position vector of the point which divides the join of points with position vectors veca+vecb and 2veca-vecb in the ratio 1:2 is

The position vector of foru points A,B,C,D are veca, vecb, 2veca+3vecb and veca-2vecb respectively. Expess the vectors vec(AC), vec(DB), vec(BC) and vec(CA) in terms of veca and vecb .