Prove that the four points `2veca+3vecb-vecc, veca-2vecb+3vecc,3veca+4vecb-2vecc and veca-6vecb+6vecc` are coplanar where `veca,vecb,vecc` are non-coplanar vectors

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.

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).

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

If |{:(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(veca.vecc,vecb.vecc,veca.vecc)| where veca, vecb,vecc are coplanar then:

The position vector of three points are 2veca-vecb+3vecc , veca-2vecb+lambdavecc and muveca-5vecb where veca,vecb,vecc are non coplanar vectors. The points are collinear when

Show that the points having position vectors (veca-2vecb+3vecc),(-2veca+3vecb+2vecc),(-8veca+13vecb) re collinear whatever veca,vecb,vecc may be

If veca,vecb,vecc are coplanar, show that veca+vecb, vecb+vecc, vecc+veca are also coplanar.

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)

If veca, vecb, vecc are non-coplanar vectors, prove that the following vectors are coplanar. (i) 3veca - vecb - 4vecc, 3veca - 2vecb + vecc, veca + vecb + 2vecc (ii) 5veca +6vecb + 7vecc, 7veca - 8vecb + 9vecc, 3veca + 20 vecb + 5vecc

Examine whather followig vectors are coplanar or nto: veca+vecb-vecc, veca-3vecb+vecc nd 2veca-vecb-vecc