For vectors $x, \: y$ in $\mathbb{R}^n$, define the inner product $\langle x, y \rangle = \Sigma^n_{i=1} x_iy_i$, and the length of $x$ to be $\| x \| = \sqrt{\langle x, x \rangle}$. Let $a, \: b$ be two vectors in $\mathbb{R} ^n$ so that $\| b \| =1$. Consider the following statements:
$\langle a, b \rangle \leq \| b \|$
$\langle a, b \rangle \leq \| a \|$
$\langle a, b \rangle = \| a \| \| b \|$
$\langle a, b \rangle \geq \| b \|$
$\langle a, b \rangle \geq \| a \|$
Which of the above statements must be TRUE of $a, \: b$? Choose from the following options.
ii only
i and ii
iii only
iv only
iv and v