If `alpha+beta+gamma =2 and veca=alphahati+betahatj+gammahatk, hatkxx (hatkxxveca)=vec0` ,then `gamma`= (A) 1 (B) -1 (C) 2 (D) none of these

If a line makes angles alpha, beta, gamma with the axes then cos2alpha +cos2beta+cos2gamma = (A) -2 (B) -1 (C) 1 (D) 2

If veca,vecb,vecc are mutually perpendicular vector and veca=alpha(vecaxxvecb)+beta(vecbxxvecc)+gamma(veccxxveca) and [veca vecb vecc]=1 then vecalpha+vecbeta+vecgamma= (A) |veca|^2 (B) -|veca|^2 (C) 0 (D) none of these

If (tan(alpha+beta-gamma))/("tan"(alpha-beta+gamma))=(tangamma)/(tanbeta),(beta!=gamma) then sin2alpha+sin2beta+sin2gamma= (a) 0 (b) 1 (c) 2 (d) 1/2

If A= [(alpha,beta),(gamma,-alpha)] is such that A^(2)=1 , then

If alpha,beta,gamma are the angle which a half ray makes with the positive direction of the axes then sin^2alpha+sin^2beta+sin^2gamma= (A) 1 (B) 2 (C) 0 (D) -1

If alpha , beta, gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If tan gamma=sec alpha sec beta+tan alpha tan beta, then cos2 gamma is necessarily (A) ge0 (B) le0 (C) lt0 (D) gt0

The value of expression of (alphatangamma+betacotgamma)(alphacotgamma+betatangamma)-4alphabetacot^2 2gamma depends on alpha (b) beta (c) gamma (d) none of these

A point (alpha, beta, gamma) satisfies the equation of the plane 3x+4y+7z=3. The value of beta , such that vecp=alphahati+betahatj+gammahatk satisfies the relation hatjxx(hatjxxvecp)=vec0 , is equal to