[Win,odd Dhamnekar]

Dipole moment  of a bond is a vector and physical quantity. It is expressed as Dipole moment[itex](\mu)=\vec{\delta \times d}[/itex] where [itex]\delta,d[/itex] means bond dipole moment and interatomic spacing respectively. In S.I. units, it is expressed in coulomb metre.

Resultant Dipole moment [itex]\mu_R (||\mu_1 +\mu_2||)[/itex] of two bond dipole moments [itex](\mu_1[/itex] and [itex]\mu_2)[/itex] acting at an angle [itex]\theta[/itex] is given by
[tex] \mu_R=\sqrt{(\mu_1 )^2+(\mu_2)^2 +2*\mu_1\cdot \mu_2 \cos{\theta}}\tag{1}[/tex]

By Law of cosines, we have [tex]||(\mu_1 -\mu_2)||=\sqrt{(\mu_1)^2 +(\mu_2)^2 - 2*\mu_1\cdot\mu_2\cos{\theta}}\tag{2}[/tex] How can we apply (2) to (1)?

[mjc123]

Why do you want to?

[Win,odd Dhamnekar]

How can we express [itex]\mu_{R}(||\mu_1 +\mu_2||)[/itex] in terms of (1)? Is the value of [itex]\mu_{R}[/itex] computed approximately? Can we prove  mathematically that vector sum =(1)?

[mjc123]

Draw a parallelogram diagram. Apply the cosine rule using the angle φ, which is the complementary angle to θ.