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

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

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecaxxvecb)xx(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)= (A) [veca vecb vecc] (B) 2[veca vecb vecc]vecr (C) 3[veca vecb vecc]vecr (D) 4[veca vecb vecc]vecr

For any four vectors, prove that ( veca × vecb )×( vecc × vecd )=[ veca vecc vecd ] vecb −[ vecb vecc vecd ] veca

if veca, vecb and vecc are there mutually perpendicular unit vectors and veca ia a unit vector then find the value of |2veca+ vecb + vecc |^2

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 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 \ a n d \ vec b are two non-collinear unit vector, and ∣ ​ veca + vecb ∣ ​ = 3 ​ then (2 veca −5 vecb ).(3 veca + vecb ) =

Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a non -zero , which is perpendicular to (veca + vecb + vecc). Now vecd = (veca xx vecb) sin x + (vecb xx vecc) cos y + 2 (vecc xx veca) . Then