44. Two lines are given by the systems of equations:

$$
\frac{x-x_{1}}{m_{1}}=\frac{y-y_{1}}{n_{1}}=\frac{z-z_{1}}{p_{1}} \quad \text { and } \quad \frac{x-x_{2}}{m_{2}}=\frac{y-y_{2}}{n_{2}}=\frac{z-z_{2}}{p_{2}}
$$

Write the condition for the parallelism of these lines. Write the condition for their perpendicularity.
44. If the lines are parallel, then their direction vectors are collinear, the direction cosines are the same, and the coefficients determining these cosines must be proportional. Hence, the condition for parallelism is:

$$
\frac{m_{1}}{m_{2}}=\frac{n_{1}}{n_{2}}=\frac{p_{1}}{p_{2}}
$$

For perpendicular lines, the scalar product of their direction vectors must be equal to 0, so we get:

$$
m_{1} m_{2}+n_{1} n_{2}+p_{1} p_{2}=0
$$

This is the condition for perpendicularity.