If OAB is a tetrahedron with edges and `hatp, hatq, hatr` are unit vectors along bisectors of
`vec(OA), vec(OB):vec(OB), vec(OC):vec(OC), vec(OA)` respectively and `hata=(vec(OA))/(|vec(OA)|), vecb=(vec(OB))/(|vec(OB)|), vec c= (vec(OC))/(|vec(OC)|)`, then :

Options

A. `([hata hatb hatc])/([hatp hatq hatr])=(3sqrt(3))/(2)`
B. `([hata+hatb" "hatb+hatc" "hatc +hata])/([hatp+hatq" "hatq+hatr" "hatr+hatp])=(3sqrt(3))/(4)`
C. `([hata+hatb" "hatb+hatc" "hatc+hata])/([hatp hatq hatr])=(3sqrt(3))/(2)`
D. `([hata hatb hatc])/([hatp +hatq" "hatq+hatr" "hatr+hatp])=(3sqrt(3))/(4)`

Answer

A, D