Find dot product of vectors $\vec{a}$ = $2\hat{i}+2\hat{j}-\hat{k}$ and $\vec{b}$ = $6\hat{i}-3\hat{j}+2\hat{k}$

Solution :

We have $\vec{a}$ = $2\hat{i}+2\hat{j}-\hat{k}$ and $\vec{b}$ = $6\hat{i}-3\hat{j}+2\hat{k}$

$\vec{a}$.$\vec{b}$ = ($2\hat{i}+2\hat{j}-\hat{k}$).($6\hat{i}-3\hat{j}+2\hat{k}$)

= (2)(6) + (2)(-3) + (-1)(2) = 12 – 6 – 2 = 4

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