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=

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 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.

If bara,barb,barc are non-coplanar vectors then [bar(a)+2bar(b)" "bar(a)+bar(c)" "bar(b)]=

If bara,barb,barc are non-coplanar vectors then [bar(a)+2bar(b)" "bar(a)+bar(c)" "bar(b)]=

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

Given four non zero vectors bar a,bar b,bar c and bar d. The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :