[填空题]
Let $\mathbf{u}=5 \mathbf{i}+2 \mathbf{j}-\mathbf{k} $ and $\mathbf{v}=2 \mathbf{i}-3 \mathbf{j}+n \mathbf{k} $ where $ n \in \mathbb{R}$ .
1. Given that $\mathbf{u}$ is perpendicular to $\mathbf{v} $, find the value of n .
Let $\mathbf{w}=7 \mathbf{i}+p \mathbf{j}-3 \mathbf{k}$ where $p \in \mathbb{R}$ .
2. Given that $|\mathbf{w}|=\sqrt{74}$ , find the possible values for p . ±
