find `x,y, and z if x veca+yvecb+zvecc=vecd and veca,vecb,vecc` are non coplanar.

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

If is given that vecx= (vecbxxvecc)/([veca,vecb,vecc]), vecy=(veccxxveca)/[(veca,vecb,vecc)], vecz=(vecaxxvecb)/[(veca,vecb,vecc)] where veca,vecb,vecc are non coplanar vectors. Find the value of vecx.(veca+vecb)+vecy.(vecc+vecb)+vecz(vecc+veca)

Show that the vectors veca-2vecb+3vecc,-2veca+3vecb-4vecc and - vecb+2vecc are coplanar vector where veca, vecb, vecc are non coplanar vectors

Solve veca.vecr=x, vecb.vecr=y, vecc.vecr=z where veca,vecb,vecc are given non coplasnar vectors.

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc) is

Statement 1: veca, vecb and vecc arwe three mutually perpendicular unit vectors and vecd is a vector such that veca, vecb, vecc and vecd are non- coplanar. If [vecd vecb vecc] = [vecdvecavecb] = [vecdvecc veca] = 1, " then " vecd= veca+vecb+vecc Statement 2: [vecd vecb vecc] = [vecd veca vecb] = [vecdveccveca] Rightarrow vecd is equally inclined to veca, vecb and vecc .

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

If veca, vecb and vecc are non-coplanar vectors, prove that the four points 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+ 6 vecc are coplanar.

Let veca =veci -veck, vecb = xveci+ vecj + (1-x)veck and vecc =y veci +xvecj + (1+x -y)veck . Then veca, vecb and vecc are non-coplanar for

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2 then (A) veca,vecb,vecc are non coplanar (B) vecb,vecc, vecd are non coplanar (C) vecb, vecd are non paralel (D) veca, vecd are paralel and vecb, vecc are parallel