315. Express through the orths $\bar{i}, \bar{j}, \bar{k}$ the orth $\overline{a^{0}}$ of the vector

$$
\bar{a}=\overline{3 i}-4 \bar{j}+6 \bar{k}
$$
Solution. It is known that the unit vector of vector $\bar{a}$ is the ratio of this vector to its modulus (see item 4 § 2), i.e.

$$
\bar{a}^{0}=\frac{\bar{a}}{a}=\frac{3 \bar{i}-4 \bar{j}+6 \bar{k}}{\sqrt{9+16+36}}=\frac{3}{7} \bar{i}-\frac{4}{7} \bar{j}+\frac{6}{7} \bar{k}
$$