In Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.

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Understand that vectors \( \mathbf{u} \) and \( \mathbf{v} \) have the same direction means \( \mathbf{u} = k \mathbf{v} \) for some scalar \( k > 0 \).

Recall that the magnitude (or norm) of a vector \( \mathbf{u} = (u_1, u_2, \ldots, u_n) \) is given by the formula: \[ \\|\mathbf{u}\\| = \sqrt{u_1^2 + u_2^2 + \cdots + u_n^2} \]

Since \( \mathbf{u} \) and \( \mathbf{v} \) have the same direction, express \( \mathbf{u} \) as \( \mathbf{u} = k \mathbf{v} \), where \( k = \frac{\\|\mathbf{u}\\|}{\\|\mathbf{v}\\|} \).

Use the given information or values of \( \mathbf{v} \) and the scalar \( k \) (if provided) to find \( \\|\mathbf{u}\\| = |k| \times \\|\mathbf{v}\\| \).

Calculate the magnitude of \( \mathbf{v} \) using the formula in step 2, then multiply by \( |k| \) to find \( \\|\mathbf{u}\\| \).

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