3. Let \( S = \{\vec{v}_1, \vec{v}_2, \dots, \vec{v}_k\} \) be an orthogonal set of nonzero vectors in a vector space \( V \). Please show that the vectors in \( S \) are linear independent. (10%)
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3. Let \( S = \{\vec{v}_1, \vec{v}_2, \dots, \vec{v}_k\} \) be an orthogonal set of nonzero vectors in a vector space \( V \). Please show that the vectors in \( S \) are linear independent. (10%)