Question on simple implications of Cauchy Schwartz inequality $|\langle x,y\rangle |\leq \|x\|\cdot \|y\| $

Question

Let $x,y \in \mathbb{R}^n$ be vectors in vector space $V$, the Cauchy Schwartz inequality states:

$$|\langle x,y\rangle |\leq \|x\|\cdot \|y\| $$

My question is:

1. The following also hold $$\langle x,y\rangle \leq \|x\|\cdot \|y\|$$

2. Is it ever possible $$\langle x,y\rangle > \|x\|\cdot \|y\|$$

Answer 1

Since $x \leq |x|$ for each $x\in\mathbb R$ the answer to the first question is yes. Since the 2nd question asks for the negation of the first its answer should be clear now aswell.