Question

Let \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{c} \) be vectors of magnitude 2, 3, and 4 respectively. If: - \( \mathbf{a} \) is perpendicular to \( (\mathbf{b} + \mathbf{c}) \), - \( \mathbf{b} \) is perpendicular to \( (\mathbf{c} + \mathbf{a}) \), - \( \mathbf{c} \) is perpendicular to \( (\mathbf{a} + \mathbf{b}) \), then the magnitude of \( \mathbf{a} + \mathbf{b} + \mathbf{c} \) is equal to:

• A. 29
• B. \( \sqrt{29} \)
• C. 26
• D. \( \sqrt{26} \)

Hint:

When vectors are perpendicular, the magnitude of their sum can be found using the Pythagorean theorem.