prove a vector equation

Question

We have to prove the following equation

I tried as

Taking square root both side and making denominator same in LHS .

After I got stuck .

Answer 1

Hint - On solving left hand side

$\left( \frac1{|\vec{a}|^2} + \frac1{|\vec{b}|^2} - 2 \frac{\vec{a}.\vec{b}}{|\vec{a}|^2.|\vec{b}|^2}\right)$

= $\left( \frac{|\vec{a}|^2 + |\vec{b}|^2 - 2 \vec{a}.\vec{b}}{|\vec{a}|^2.|\vec{b}|^2} \right)$

= $\left( \frac{\vec{a} - \vec{b}}{|\vec{a}|.|\vec{b}|} \right)^2$

As $\vec a^2 = |\vec a|^2$