If O be the origin the vector `vec(OP)` is called the position vector of point P. Also `vec(AB)=vec(OB)-vec(OA)`. Three points are said to be collinear if they lie on the same stasighat line.Points A,B,C are collinear if one of them divides the line segment joining the others two in some ratio. Also points A,B,C are collinear if and only if `vec(AB)xxvec(AC)=vec0` Let the points A,B, and C having position vectors `veca,vecb and vecc` be collinear Now answer the following queston: `tveca+svecb=(t+s)vecc` where t and s are scalar (A) `tveca+svecb=(t+s)vecc` where t and s are scalar (B) `veca=vecb` (C) `vecb=vecc` (D) none of these

If O be the origin the vector vec(OP) is called the position vector of point P. Also vec(AB)=vec(OB)-vec(OA) . Three points are said to be collinear if they lie on the same stasighat line.Points A,B,C are collinear if one of them divides the line segment joining the others two in some ratio. Also points A,B,C are collinear if and only if vec(AB)xxvec(AC)=vec0 Let the points A,B, and C having position vectors veca,vecb and vecc be collinear Now answer the following queston: (A) veca.vecb=veca.vecc (B) vecaxxvecb=vecc (C) vecaxxvecb+vecbxxvecc+veccxxveca=vec0 (D) none of these

If O be the origin the vector vec(OP) is called the position vector of point P. Also vec(AB)=vec(OB)-vec(OA) . Three points are said to be collinear if they lie on the same stasighat line.Points A,B,C are collinear if one of them divides the line segment joining the others two in some ratio. Also points A,B,C are collinear if and only if vec(AB)xxvec(AC)=vec0 Let the points A,B, and C having position vectors veca,vecb and vecc be collinear Now answer the following queston: The exists scalars x,y,z such that (A) xveca+yvecb+zcvecc=0 and x+y+z!=0 (B) xveca+yvecb+zcvecc!=0 and x+y+z!=0 (C) xveca+yvecb+zcvecc=0 and x+y+z=0 (D) none of these

Prove that the points A,B and C with position vectors vec a,vec b and vec c respectively are collinear if and only if vec a xxvec b+vec b xxvec c+vec c xxvec a=vec 0

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

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

Three points with position vectors vec(a), vec(b), vec(c ) will be collinear if there exist scalars x, y, z such that

If vec a,vec b are the position vectors of the points (1,-1),(-2,m), find the value of m for which vec a and vec b 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 .

If a,b,c are non coplanar vectors prove that the points having the following position vectors are collinear: vec a,vec b,3vec a-2vec b

Vectors vec a and vec b are non-collinear.Find for what value of n vectors vec c=(n-2)vec a+vec b and vec d=(2n+1)vec a-vec b are collinear?