When does equality hold in $\bigg(\sum_{k=1}^na_k^2\bigg)\bigg(\sum_{k=1}^nb_k^2\bigg)\ge\bigg(\sum_{k=1}^na_kb_k\bigg)^2$

Question

In the Cauchy-Schwarz inequality:$$\bigg(\sum_{k=1}^na_k^2\bigg)\bigg(\sum_{k=1}^nb_k^2\bigg)\ge\bigg(\sum_{k=1}^na_kb_k\bigg)^2$$If $a=<a_1,a_2,...,a_n>$ and $b=<b_1,b_2,...,b_n>$ then $(a\cdot b)^2\le ||a||^2||b||^2$

When does equality occur?

Is the answer when $a$ and $b$ are linear independent? Am I even on the right track?

Answer 1

When the $a_i$ and $b_i$ are proportional - if there is a $c$ such that $a_i = c b_i$ for all $i$.