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Section 11.3 : 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.

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