Question

Electron pairs will repel each other. Then why, the dipole moment arrow always points towards lone pair. Since niyrogen has protons also, why arrow pointing towards lone pair??

Answer 1

The lone pairs don't contribute to the dipole. The dipole moment is determined by the differences in the electronegativity of the atoms. The lone pairs do effect the global geometry for the molecule, which affects the net dipole. For NH3 or NF3, for example, the lowest energy conformation is non planar which results in a net dipole moment going straight through the C3 axis lying in the plane of the lone pair and nitrogen.