Exercise 9

Suppose that $\vvec_1$, $\vvec_2$, and $\vvec_3$ are three nonzero vectors that are pairwise orthogonal; that is, each vector is orthogonal to the other two.

1. Explain why $\vvec_3$ cannot be a linear combination of $\vvec_1$ and $\vvec_2$.

2. Explain why this set of three vectors is linearly independent.