If `bar b,bar c` are two unit vectors along the positive `x, y` axes, and `bar a` is any vector, then `(bar a*bar b)bar b+(bar a*bar c)bar c+(bar a*(bar b xx bar c))/(|bar b xx bar c|) (bar b xx bar c)=`

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, bar b, bar c are three vectros, then prove that: (bar a xx bar b) xx bar c = (bar a. bar c) bar b-(bar b. bar c) bar a.

For three vectors bar(a),bar(b) and bar( c ),bar(a)xx(bar(b)xx bar( c ))=(bar(a)xx bar(b))xx bar( c ) then

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 4bar(a)+5bar(b)+9bar( c )=0 then (bar(a)xx bar(b))xx[(bar(b)xx bar( c ))xx(bar( c )xx bar(a))] = ………..

If four vectors bar(a),bar(b),bar(c),bar(d) are coplanar,then (bar(a)xxbar(b))xx(bar(c)xxbar(d))=

(bar(a)+bar(b))xx(bar(a)-bar(b))+(bar(b)+bar(c))xx(bar(b)-bar(c))+(bar(c)+bar(a))xx(bar(c)-bar(a))=

(bar(a)+2bar(b)-bar(c))*(bar(a)-bar(b))xx(bar(a)-bar(bar(c)))=

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