If `x(bar a xx bar b)+y(bar b xx bar c)+z(bar c xx bar a)=bar r and [bar a bar b bar c]=1/8` then `x+y+z=`

If x(bar(a)xxbar(b))+y(bar(b)xxbar(c))+z(bar(c)xxbar(a))=bar(r) and [bar(a)bar(b)bar(c)]=(1)/(8) then x+y+z=

If bar r=l(bar b xx bar c)+m(bar c xx bar a)+n(bar a xx bar b) and [bar a bar b bar c]=2 , then l+m+n is equal to

bar(d)=lambda(bar(a)xx bar(b))+mu(bar(b)xx bar( c ))+v(bar( c )xx bar(a)) and [bar(a)bar(b)bar( c )]=(1)/(8) then lambda+mu+v = …………..

Prove that [[bar a xx bar p, bar b xx bar p, bar cxx bar r]]+[[bar axx bar q, bar b xx bar r, bar c xx bar p]]+[[bar a xx bar r, bar b xx bar p,bar c xx bar q]]=0

If bar a = 2 bar I + bar j - bar k, bar b = - bari + 2 bar j - 4 bar k and bar c = bar I + bar j + bar k , then find ( bar a xx bar b) cdot (bar b xx bar c) .

Let bar a,bar b,bar c be three non-coplanar vectors and bar d be a non-zero vector, which is perpendicularto bar a+bar b+bar c . Now, if bar d= (sin x)(bar a xx bar b) + (cos y)(bar b xx bar c) + 2(bar c xx bar a) then minimum value of x^2+y^2 is equal to

if bar a+2 bar b+3bar c=bar 0 then bar axxbar b+bar b xx bar c+bar cxx bara = lambda (bar b xx bar c) ,where lambda=

[bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

Show that (bar(a)+bar(b)) . [(bar(b)+bar(c)) xx (bar(c )+bar(a))] = 2[bar(a)bar(b)bar(c )] .