Show that the point `A ,B ,C` with position vectors ` vec a-2 vec b+3 vec c ,2 vec a+3 vec b-4 vec c` and `-7 vec b+10 vec c` are collinear.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b+2vec c and -8vec a+13vec b are collinear whatever be vec a,vec b,vec c .

Show that the points A,B,C with position vectors 2vec a+3vec b+5vec c,vec a+2vec b+3vec c and 7vec a-vec c respectively,are collinear.

The points with position vectors vec a-2vec b+3vec c,2vec a+lambdavec b-4vec c,-7vec b+10vec c will be collinear if lambda=...cdots

Show that the points whose position vectors are vec(a) + 2vec(b) + 5vec(c), 3vec(a) + 2vec(b) + vec(c), 2vec(a) + 2vec(b) + 3vec(c) are colliner.

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

vec a * {(vec b + vec c) xx (vec a + 2vec b + 3vec c)} = [vec with bvec c]

Show that the found points A,B,C,D with position vectors vec a,vec b,vec c,vec d respectively such that 3vec a-2vec b+5vec c-6vec d=vec 0 ,are coplanar .Also,find the position vector of the point of intersection of the line segments AC and BD.

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

Show that the points having position vectors (-2vec(a) + 3 vec(b)+5vec(c)),(vec(a)+ 2 vec(b)+ 3 vec(c)) and (7vec(a)- vec(c)) are collinear, whatever be vec(a),vec(b),vec(c).