`[bar a xx bar b` `bar c xx bar d` ` bar e xx bar f]` is equal to

If bar = hat i + hat j and bar b = 2 hat i - hat k then the intersection piont of the lines bar r xx bar a = bar b xx bar a and bar r xx bar b = bar a xx bar b is .............

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 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

If bar(a), bar(b), bar(c ) respresents the vertices A, B, and C respectively of DeltaABC then prove that |(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))| is twice the area of DeltaABC .

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=

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

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 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) .

If bar(a)bar(b)bar(c ) and bar(d) are vectors such that bar(a) xx bar(b) = bar(c ) xx bar(d) and bar(a) xx bar(c ) = bar(b)xxbar(d) . Then show that the vectors bar(a) - bar(d) and bar(b) -bar(c ) are parallel.