Prove that for any nonzero scalar a the vectors `aveci+2avecj-3aveck, (2a+1)veci+(2a+3)vecj+(a+1)veck and (3a+5)veci+(a+5)vecj+(a+2)veck` are non 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

A unit vector coplanar with veci + vecj + 2veck and veci + 2 vecj + veck and perpendicular to veci + vecj + veck is _______

Prove that the four points 4veci+5veci+veck, -(vecj+veck),3veci+9vecj+4veck and 4(-veci+vecj+veck) are coplanar

Find the value of the constant lamda so that vectors veca=vec(2i)-vecj+veck, vecb=veci+vec(2j)-vec(3j), and vecc=vec(3i)+vec(lamdaj)+vec(5k) are coplanar.

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

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.

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 veca, vecb, vecc are non coplanar vectors and lamda is a real number, then the vectors veca+2vecb+3vecc, lamdavecb+4vecc and (2lamda-1)vecc are non coplanar for

If veca, vecb, vecc are non coplanar vectors and lamda is a real number, then the vectors veca+2vecb+3vecc, lamdavecb+4vec and (2lamda-1)vecc are non coplanar for

If vecA=2veci+3vecj+4veck and vecB=4veci+3vecj+2veck, find vecAxxvecB .