If ` vec a , vec b ` and ` vec c` are any three non-coplanar vectors, then prove that points are collinear: ` veca+ vecb+vecc , 4veca+3vecb ,10veca+7vec b-2vecc` .

If vec a , vec ba n d vec c are three non coplanar vectors, then ( veca + vecb + vecc )[( veca + vecb )×( veca + vecc )] is :

i. If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3veca -7vecb -4 vecc ,3 veca -2vecb + vecc and veca + vecb +2 vecc are coplanar.

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors and vec r is any vector in space, then ( veca × vecb )×( vecr × vecc )+( vecb × vecc )×( vecr × veca )+( vecc × veca )×( vecr × vecb ) is equal to

If vec a , vec ba n d vec c are three non-zero non-coplanar vectors, then the value of (veca.veca)vecb×vecc+(veca.vecb)vecc×veca+(veca.vecc)veca×vecb.

If veca,vecb ,vecc are any three non- coplanar vectors then the equation [vecbxxvecc veccxxveca vecaxxvecb]x^(2) + [veca+vecb vecb+vecc vecc+veca] x+1 +[vecb-vecc vecc -veca veca -vecb] =0 has roots (A) real and distinct (B) real (C) equal (D) imaginary

veca , vecb and vecc are three non-coplanar vectors and vecr . Is any arbitrary vector. Prove that [vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr .

If a ,ba n dc are three non-cop0lanar vector, non-zero vectors then the value of ( veca . veca ) vecb × vecc +( veca . vecb ) vecc × veca +( veca . vecc ) veca × vecb .

If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is perpendicular to veca xx (vecb xx vecc) , then the value of [ veca xx ( vecb xx vecc)] xx vecc is equal to

If veca, vecb and vecc are three non-coplanar vectors, then find the value of (veca.(vecbxxvecc))/(vecb.(veccxxveca))+(vecb.(veccxxveca))/(vecc.(vecaxxvecb))+(vecc.(vecbxxveca))/(veca.(vecbxxvecc))