The position vectors of the points A,B,C are `vec a, vec b, vec c` respectively. If `3 vec a + 2 vec c= 5 vecb`, are the points A,B,and C collinear? If so find `AB:BC`.

If the position vectors of the points A(3,4),B(5,-6) and (4,-1) are vec a,vec b,vec c respectively compute vec a+2vec b-3vec c

The position vector of A,B are vec a and vec b respectively.The position vector of C is (5(vec a)/(3))-vec b then

If the position vectors of three points are vec a-2vec b+3vec c,2vec a+3vec b-4vec c,-7vec b+10vec c then the three points are

Statement 1: if three points P,Q and R have position vectors vec a,vec b, and vec c ,respectively, and 2vec a+3vec b-5vec c=0, then the points P,Q, and R must be collinear.Statement 2: If for three points A,B, and C,vec AB=lambdavec AC, then points A,B, and C must be collinear.

If the position vector of these points are vec(a) -vec(b)+3 vec(c ), 2 vec(a)+3vec(b)-4 vec( c) ,-7 vec(b) + 10 vec(c ) , then the three points are

Let position vectors of points A,B and C are vec a,vec b and vec c respectively.Point D divides line segment BCinternally in the ratio 2:1. Find vector vec AD.

The position vectors of three points are 2vec a-vec b+3vec c,vec a-2vec b+xvec c and yvec a-5vec b where vec a,vec b,vec c are non coplanar vectors.If the three points are collinear then

The position vector of three points are 2vec a-vec b+3vec c,vec a-2vec b+lambdavec c and muvec a-5vec b where vec a,vec b,vec c are noncoplanar vectors.The points are collinear when

If vec a,vec b,vec c are position vectors o the point A,B, and C respectively,write the value of vec AB+vec BC+vec AC

Let vec(a).vec(b) and vec(c ) be the position vectors of points A,B and C, respectively. Under which one of the following conditions are the points A, B and C collinear?