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:
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:
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When vectors are in equilibrium, the sum of their dot products often equals zero.
Updated On: Jan 6, 2026
- \( m \leq 0 \)
- \( m>0 \)
- \( m = 0 \)
- \( m = 3 \)
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The Correct Option is C
Solution and Explanation
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: \[ \boxed{0} \]
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: \[ \boxed{0} \]
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