[QUE/VS-08003]

Prove that the following inequalities hold in every inner product space

1. \( \Big| x-y \Big| \le \Vert x\Vert + \Vert y\Vert \);
2. \( \Big|x-y\Big| \ge \Vert x\Vert - \Vert y\Vert \).
3. \( \Big| \sum_{i=1}^n x_i \Big| \le \sum_{i=1}^n \Vert x_i\Vert \);