Let `bar a,bar b ,bar c` be vectors of equal magnitude such that the angle between `bar a and bar b` is `alpha, bar b and bar c` is `beta and bar c and bar a` is `gamma` . Then the minimum value of `cos alpha + cos beta + cos gamma` is

If bar(a),bar(b),bar (c ) are pair wise mutually perpendicular vectors of equal magnitude , then the angle wisv bar(a)+bar(b)+bar (c ) is

IF bar a , bar b , bar c are mutually perpendicular vectors having magnitudes 1,2,3 respectively then [ bar a + bar b + bar c " " bar b - bar a " " bar c ]=?

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.

Let bar(a),bar(b),bar(c) be unit vectors such that bar(a)*bar(b)=bar(a).bar(c)=0 and the angle between bar(b) and bar(c) is (pi)/(6) if bar(a)=n(bar(b)xxbar(c)), then value of n is

Given that bar(a) and bar(b) are two unit vectors such that angle between bar(a) and bar(b) is cos ^(-1)((1)/(4)). If bar(c) be a vector in the plane of bar(a) and bar(b), such that |vec c|=4,vec c xxvec b=2vec a xxvec b and vec c=lambdavec a+mubar(b) then,find

If bar(a),bar(b),bar(c) are three vectors of magnitude sqrt(3),1,2 such that bar(a)xx(bar(a)xxbar(c))+3bar(b)=bar(0) and theta is the angle between bar(a) and bar(c) then cos^(2)theta=

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

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 :