Question

Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors with magnitudes 4, 4, and 2, respectively. If \( \vec{a} \) is perpendicular to \( (\vec{b} + \vec{c}) \), \( \vec{b} \) is perpendicular to \( (\vec{c} + \vec{a}) \), and \( \vec{c} \) is perpendicular to \( (\vec{a} + \vec{b}) \), then the value of \( |\vec{a} + \vec{b} + \vec{c}| \) is:

• A. 3
• B. 6
• C. \( \sqrt{6} \)
• D. \( \sqrt{6} \)
• E. -6

Hint:

For three mutually perpendicular vectors, the resultant magnitude is the square root of the sum of their squared magnitudes.

Answer 1

The Correct Option is B

Given that the vectors are mutually perpendicular, we can use the formula: \[ |\vec{a} + \vec{b} + \vec{c}| = \sqrt{|\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2} \] Substituting the magnitudes: \[ |\vec{a} + \vec{b} + \vec{c}| = \sqrt{4^2 + 4^2 + 2^2} = \sqrt{16 + 16 + 4} = \sqrt{36} = 6 \]