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: 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: 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+zvecc=0 and x+y+z=0 (D) none of these

Prove that the points A ,Ba n d C with position vectors vec a , vec ba n d vec c respectively are collinear if and only if vec axx vec b+ vec bxx vec c+ vec cxx vec a= vec0dot

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

The position vector of the point which divides the line segment joining the points with position vectors 2 vec(a) = 3b and vec(a) + vec(b) in the ratio 3:1 is

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 four points A ,B , Ca n dD with position vectors vec a , vec b , vec c and vec d respectively are coplanar if and only if 3 vec a-2 vec b+ vec c-2 vec d=0.

If a and b are position vectors of A and B respectively the position vector of a point C on AB produced such that vec(AC)=3 vec(AB) is

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 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.