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### Section 5-3 : Dot Product

3. Determine the dot product, $$\vec a\centerdot \vec b$$ if $$\left\| {\vec a} \right\| = 5$$, $$\displaystyle \left\| {\vec b} \right\| = \frac{3}{7}$$ and the angle between the two vectors is $$\displaystyle \theta = \frac{\pi }{{12}}$$.

Show Solution

Not really a whole lot to do here. We just need to run through the formula from the geometric interpretation of the dot product.

$\vec a\centerdot \vec b = \left( 5 \right)\left( {\frac{3}{7}} \right)\cos \left( {\frac{\pi }{{12}}} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{2.0698}}$