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Question
Find \[\vec{a} \cdot \vec{b}\] when
\[\vec{a} =\hat{i} - 2\hat{j} + \hat{k}\text{ and } \vec{b} = 4 \hat{i} - 4\hat{j} + 7 \hat{k}\]
Solution
We have
\[ \vec{a} = \hat{i} - 2 \hat{j}+ \hat{k}\text{ and } \vec{b} = 4 \hat{i} - \hat{j} +7 \hat{k}\]
\[ \vec{a} . \vec{b} =\left( \hat{i}- 2 \hat{j} + \hat{k}\right) . \left( 4 \hat{[i} - \hat{j}+7 \hat{k}\right)\]
\[ = \left( 1 \right)\left( 4 \right) + \left( - 2 \right)\left( - 4 \right) + \left( 1 \right)\left( 7 \right)\]
\[ = 4 + 8 + 7\]
\[ = 19\]
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