Prove that `[bara times barb bara times barc bard]=(bara.bar d)[bara barb barc]`

IF barx times barb=barc times barb and barx . bara =0 then barx=

If vectors barb, bar c ,bard are not coplanar then prove that (bara times barb) times (barc times overlind)+(bara times barc) times (bard times barb)+(bara times bard) times (barb times barc) is parallel to bara .

If barc=bara times barb and barb=barc times bara then

IF bar(a),bar(b),bar(c ) are vectors from the origin to three points A,B,C show that bara times barb +barb times barc+barc times bara is perpendicular to the plane ABC.

If hatd is a unit vectors such that hatd=lamdabarb times barc+mubarc times bara+vbara times barb then |(hatd.bara)(barb times barc)+(bard.barb) (barc times bara)+(bard.barc) (bara times barb)| is equal to

If bara,barb,barc are non-coplanar vectors, express bara times (barb times barc) as a linear combination of bara,barb,barc

Let bara,barb and barc are three mutually perpendicular unit vectors and a unit vector barr satisfying the equation (barb - barc) times (barr times bara)+(barc - bara) times (barr times barb)+(bara-barb) times (barr -barc)=0 then barr is

bara times (barb times barc) +barb times (barc times bara)+ barc times (bara times barb) equals

For three non-coplanar vectors bara,barb,barc the relation |(bara times barb).barc|=|bara||barb||barc| holds true , if

If bara ,barb and barc are three unit vectors such that bara times (barb times barc)=1/2 barb Find the angles which bara makes with barb and barc .