`vecu, vecv and vecw` are three nono-coplanar unit vectors and `alpha, beta and gamma` are the angles between `vecu and vecu, vecv and vecw and vecw and vecu`, respectively and `vecx , vecy and vecz` are unit vectors along the bisectors of the angles `alpha, beta and gamma.` respectively, prove that `[vecx xx vecy vecy xx vecz vecz xx vecx) = 1/16 [ vecu vecv vecw]^(2) sec^(2) alpha/2 sec^(2) beta/2 sec^(2) gamma/2`.

vec u , vec v and vec w are three non-coplanar unit vecrtors and alpha,beta and gamma are the angles between vec u and vec v , vec v and vec w ,a n d vec w and vec u , respectively, and vec x , vec y and vec z are unit vectors along the bisectors of the angles alpha,betaa n dgamma , respectively. Prove that [ vecx xx vec y vec yxx vec z vec zxx vec x]=1/(16)[ vec u vec v vec w]^2sec^2(alpha/2)sec^2(beta/2)sec^2(gamma/2) .

If vecu and vecv are unit vectors and theta is the acute angle between them, then 2 vecu xx 3vecv is a unit vector for

If vecu and vecv are unit vectors and theta is the acute angle between them, then 2 vecu xx 3vecv is a unit vector for

If vecu and vecv are unit vectors and theta is the acute angle between them, then 2 uvecu xx 3vecv is a unit vector for

If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbers then the equality [3vecu p vecv p vecw]-[p vecv vecw qvecu]-[2vecw-qvecv qvecu]=0 holds for

Given that vecx + vecy = vecz and x + Y =z , Then the angle between vecx and vecy is

If the direction angles of a line are alpha, beta and gamma respectively, then cos 2 alpha + cos 2 beta + cos 2gamma is equal to

If veca and vecb are two non collinear vectors and vecu = veca-(veca.vecb).vecb and vecv=veca x vecb then vecv is

Let veca ,vecb , vecc be three unit vectors such that angle between veca and vecb is alpha , vecb and vecc " is " beta and vecc and veca " is " gamma. " if " | veca. + vecb + vecc| =2 , then cos alpha + cos beta + cos gamma =

Let vecu and vecv be unit vectors such that vecu xx vecv + vecu = vecw and vecw xx vecu = vecv . Find the value of [vecu vecv vecw ]