If `vecu, vercv, vecw` be three noncoplanar unit vectors and `alpha,beta, gamma` the angles between `vecu`and `vecv, vecv` and `vecw,vecw` and `vecu` respectively, `vecx, vecy , vecz` unit vector along the bisectors of the angles `alpha, beta, 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`

If hat u , hat v , hat w be three non-coplanar unit vectors with angles between hat u& hat v is alpha between hat v& hat w is beta and between hat w& hat u is gamma . If vec a , vec b , vec c are the unit vectors along angle bisectors of alpha,beta,gamma respectively, then prove that [ vec ax vec b vec bx vec c vec cx vec a]=1/(16)[ hat u hat v hat w]^2sec^2(alpha/2)sec^2(beta/2)sec^2(gamma/2)

If vecu, vecv, vecw are three non-coplanar vectors, the (vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw) equals

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

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, and vecw are three non-caplanar vectors, then prove that (vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw)=vecu.vecvxxvecw

Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + vecw = veca, vecuxx (vecv xx vecw)= vecb, (vecu xx vecv) xx vecw= vecc, vec a.vecu=3//2, veca.vecv=7//4 and |veca|=2 Vector vecu is

If vecu, vecv, vecw are three vectors such that [vecu vecv vecw]=1 , then 3[vecu vecv vecw]-[vecv vecw vecu]-2[vecw vecv vecu]=

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 ]