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Section 11.3 : Dot Product

2. Determine the dot product, \(\vec a\centerdot \vec b\) if \(\vec a = \left\langle {0,4, - 2} \right\rangle \) and \(\vec b = 2\vec i - \vec j + 7\vec k\).

Show Solution

Not really a whole lot to do here. We just need to run through the definition of the dot product and do not get excited about the “mixed” notation here. We know that they are equivalent notations!

\[\vec a\centerdot \vec b = \left( 0 \right)\left( 2 \right) + \left( 4 \right)\left( { - 1} \right) + \left( { - 2} \right)\left( 7 \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 18}}\]