When does the equality NOT occur?

Algebra Level 3

Which of the following is the domain of $(a_1,a_2,…,a_n )$ and $(b_1,b_2,…,b_n )$ , such that we will always have

$(a_1^2+a_2^2+⋯+a_n^2 )(b_1^2+b_2^2+⋯+b_n^2 )≥(a_1 b_1+a_2 b_2+⋯+a_n b_n )^2$

In the responding domain, which of the following is true such that the equality does not always occur?

a_1=a_2=...=a_n

b_1=b_2=...=b_n

a_i=b_i

The sequence of

a

and

b

is a G.P with the same common ratio. The sequence of

a

and

b

is an A.P with the same common difference.

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