313. Find the scalar product of the vectors

$$
\bar{p}=\bar{i}-3 \bar{j}+\bar{k}, \bar{q}=\bar{i}+\bar{j}-4 \bar{k}
$$
Solution. The scalar product of the vectors will be found using formula (12):

$$
\bar{p} \bar{q}=1 \cdot 1+(-3) \cdot 1+1 \cdot (-4)=-6
$$