Prove that the points A,B,C wth positon vectros `veca,vecb,vecc` are collinear if and only if `(vecbxxvecc)+(veccxxveca)+(vecaxxvecb)=vec0`

If the three vectors veca,vecb,vecc are non coplanar express each of vecbxxvecc, veccxxveca, vecaxxvecb in terms of veca,vecb,vecc .

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Prove that vecaxx(vecbxxvecc)+vecbxx(veccxxveca)+veccxx(vecaxxvecb)=vec0

Assertion: Three points with position vectors vecas,vecb,vecc are collinear if vecaxxvecb+vecbxxvecc+veccxxveca=0 Reason: Three points A,B,C are collinear Iff vec(AB)xxvec(AC)=vec0 (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

For three vectors veca+vecb+vecc=0 , check if (vecaxxvecb)=(vecbxxvecc)=(veccxxveca)

Three points whose position vectors are veca,vecb,vecc will be collinear if (A) lamdaveca+muvecb=(lamda+mu)vecc (B) vecaxxvecb+vecbxxvecc+veccxxveca=0 (C) [veca vecb vecc]=0 (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 veca, vecb, vecc are three vectors, then [(vecaxxvecb, vecbxxvecc, veccxxveca)]=

If veca,vecb,vecc are coplanar then show that vecaxxvecb, vecbxxvecc and veccxxveca are also coplanar.