Step 1 :The first statement is asking if an orthogonal set of vectors is necessarily linearly independent. Orthogonal vectors are vectors that are at right angles to each other. In other words, the dot product of any two vectors in the set is zero. Linearly independent vectors are vectors that cannot be written as a linear combination of the other vectors in the set. If a set of vectors is orthogonal, then it must be linearly independent. This is because if a vector could be written as a linear combination of the other vectors, then it would not be at right angles to them. Therefore, the first statement is True.
Step 2 :Final Answer: The statement "If the set \(\left\{\vec{u}_{1}, \vec{u}_{2}, \vec{u}_{3}\right\} is orthogonal, then it must be linearly independent" is \(\boxed{True}\).