QuestionQuestion 7: Let $\left\{\boldsymbol{u}_{1}, \boldsymbol{u}_{2}, \boldsymbol{u}_{3}\right\}$ be an orthonormal basis for a three-dimensional subspace $S$ of an inner product space $V$, and let $$\boldsymbol{x}=2 \boldsymbol{u}_{1}-\boldsymbol{u}_{2}+\boldsymbol{u}_{3} \quad \text { and } \quad \boldsymbol{y}=\boldsymbol{u}_{1}+\boldsymbol{u}_{2}-4 \boldsymbol{u}_{3} .$$ a) Determine the value of $\langle\boldsymbol{x}, \boldsymbol{y}\rangle$. b) Determine the value of $\|\boldsymbol{x}\|$.