If hat u , hat v , hat w be three non-c...

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)`

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