IF `bara=hati+hatj+hatk,barb=2hatj-hatk and barr times bara=barb times bara,barr . barb`=0 then `barr/|barr|` is equal to

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

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

If bara=hati+hatj+hatk , bara.barb=2 and bara times barb=2hati+hatj-3hatk then

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

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

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

Let a=hati - hatj, b=hati + hatj + hatk and c be a vector such that a xx c + b=0 and a.c =4, then |c|^(2) is equal to .

IF |bara|=4,|barb|=2 and the angle between bara and barb is pi/6 then (bara times barb)^2=

(bara times hati)^2+(bara+hatj)^2+(bara times hatk)^2 is equal to