Chapter 5 - Inner Product Spaces - 5.2 Orthogonal Sets of Vectors and Orthogonal Projections - Problems - Page 361: 33

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Let $\{u1, u2, v\}$ be linearly independent vectors in an inner product space V, and suppose that $u_1$ and $u_2$ are orthogonal. Prove: $\\ \leftrightarrow < v+\lambda u_1+\mu u_2,u_1>=0\\ \leftrightarrow < v+ u_1>++=0 \\ \leftrightarrow < v+ u_1>+\lambda +\mu =0 \\ \leftrightarrow < v+ u_1>+\lambda ||u_1||^2=0 \\ \rightarrow \lambda=-\frac{}{||u_1||^2}$ $\\ \leftrightarrow < v+\lambda u_1+\mu u_2,u_2>=0\\ \leftrightarrow < v+ u_2>++=0 \\ \leftrightarrow < v+ u_2>+\lambda +\mu =0 \\ \leftrightarrow < v+ u_2>+\mu ||u_2||^2=0 \\ \rightarrow \mu=-\frac{}{||u_2||^2}$