Question

If \( a, b, c \) are three non-zero vectors such that \( a + b + c = 0 \) and \( m = a \cdot b + b \cdot c + c \cdot a \), then:

• A. \( m \leq 0 \)
• B. \( m>0 \)
• C. \( m = 0 \)
• D. \( m = 3 \)

Hint:

When vectors are in equilibrium, the sum of their dot products often equals zero.

Answer 1

The Correct Option is C

Step 1: Use the given relations.
The condition \( a + b + c = 0 \) implies that the vectors are in equilibrium. The dot products give the value of \( m = 0 \).
Step 2: Conclusion.
Thus, \( m = 0 \).
Final Answer: \[ \boxed{0} \]