Question

If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of \( |\vec{a} + \vec{b} + \vec{c}|^2 \) is:

• A. \( |\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2 \)
• B. \( |\vec{a}| + |\vec{b}| + |\vec{c}| \)
• C. \( 2(|\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2) \)
• D. \( \frac{1}{2}(|\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2) \)
• E. \( 0 \)

Hint:

This geometric condition essentially means that the vectors \( \vec{a}, \vec{b}, \vec{c} \) behave like the axes of a coordinate system (mutually orthogonal) in terms of their dot products summing to zero.

Answer 1

The Correct Option is A