Given: If $|\vec{a}| = 3, |\vec{b}| = 4, |\vec{c}| = 5$ and $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, find $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$. Step 1: Formulate initial mathematical setup / substitution: Given equation / conditions: $$Square both sides: 9 + 16 + 25 + 2 S$$ [1.0 Mark] Step 2: Perform intermediate algebraic / calculus operations: Executing the step-by-step reduction: $$> S$$ [1.0 Mark] Step 3: Evaluate final values / boundary conditions: Substituting limits or solving the simplified system: $$-25.$$ [1.0 Mark] Conclusion: The final evaluated answer is -25..
--- 🎯 Official CBSE Marking Scheme: Formulating mathematical relation: 1.0 Mark Executing algebraic/calculus operations: 1.0 Mark Evaluating final solution/vector: 1.0 Mark
Correct Answer:
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