Discussion
If \(\vec{a}.\vec{b} = 12\), then \((3\vec{a}).(3\vec{b})\) is equal to
Answer: C
The value is 108.
Each scalar comes out of the dot product.
\[ \begin{aligned} (3\vec{a}).(3\vec{b}) &= 9(\vec{a}.\vec{b}) \\ &= 9 \times 12 = 108 \end{aligned} \]
36 takes the factor 3 out only once, and 144 squares the dot product instead of the scalar. 4 and 16 divide instead of multiplying.
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