Normalization coefficient of sp2 hybrid orbital

[gerrardz]

How to obtain the coefficients of normalized wavefunction for the hybrid orbital in sp₂ hybridization (esp in BH₃) , which normally in surds? In what way symmetry affect the linear combination of the atomic orbitals ? Will appreciate if anyone could help or provide some beginning guides , thanks a lot

 

[gerrardz]

thanks God, i managed to answer myself : first by vectorially resolving the p orbitals in trigonal direction, then propose linear combination to s orbital, then apply normalization rule to the wave functions to generate 1st equation , then apply orthogonality of different orbitals to obtain 2nd equation. Eventually simultaneously solve all the coefficients at once.
Can anyone confirm my method ? Or offer some shortcut , thanks.