Question:
If $\vec{a} \cdot \vec{b}=12$, then $(3\vec{a}) \cdot (3\vec{b})$ is equal to:
If $\vec{a} \cdot \vec{b}=12$, then $(3\vec{a}) \cdot (3\vec{b})$ is equal to:
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Multiply all scalars together before multiplying with the dot product result.
Updated On: Apr 28, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Concept
Using scalar properties of dot products: $(k_1\vec{a}) \cdot (k_2\vec{b}) = k_1 k_2 (\vec{a} \cdot \vec{b})$.
Step 2: Analysis
Given $k_1 = 3, k_2 = 3$ and $\vec{a} \cdot \vec{b} = 12$.
Step 3: Calculation
$(3\vec{a}) \cdot (3\vec{b}) = 3 \times 3 \times (\vec{a} \cdot \vec{b}) = 9 \times 12 = 108$. Final Answer: (C)
Using scalar properties of dot products: $(k_1\vec{a}) \cdot (k_2\vec{b}) = k_1 k_2 (\vec{a} \cdot \vec{b})$.
Step 2: Analysis
Given $k_1 = 3, k_2 = 3$ and $\vec{a} \cdot \vec{b} = 12$.
Step 3: Calculation
$(3\vec{a}) \cdot (3\vec{b}) = 3 \times 3 \times (\vec{a} \cdot \vec{b}) = 9 \times 12 = 108$. Final Answer: (C)
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