Show that the vectors `bara - 2barb + 3barc,- 2bara + 3barb - 4barc` and `bara - 3barb + 5barc` are coplanar, where a, b, c are non- coplanar vectors.

Show that the four points -bara+ 4barb - 3barc, 3bara +2barb-5barc,-3bara +8barb -5barc and -3bara + 2barb + barc are coplanar, where bara,barb,barc are non - coplanar vectors.

[bara barb barc]+[bara barc barb] =

Show that [2bara +barb +barc bara +2barb +barc bara +barb +2barc] = 4[bara barb barc]

If bara. barb = barb. barc = barc . bara = 0 then [bara barb barc] =

If kbara = 3barb+2barc, bara=-2barb+5barc " and if " barb and barc have opposite direction, then

If bara,barb,barc are non-coplanar vectors, prove that points with position vectors 2bara+3barb-barc,bara-2barb+3barc,3bara+4barb-2barc and bara - 6barb + 6barc are coplanar.

If bara,barb,barc are non-coplaner, then show that the vectors bara -bar b , barb + barc ,bar c + bara are coplanar

bara , barb, barc are coplanar vectors . Prove that of the following four points are coplanar. 6bara + 2barb - barc , 2bara - barb +3barc , - bara + 2barb - 4barc , - 12bara - barb - 3barc .

i) Let bara, barb and barc be non - coplanar vectors and baralpha=bara+2barb+3barc,barbeta=2bara+barb-2barc and bargamma=3bara-7barc , then find [baralphabarbetabargamma] (ii) If bara,barbbarc are non coplanar vectors, then find ((bara+2barb-barc).[(bara-barb)xx(bara-barb-barc)])/([barabarbbarc])