$\"\"$

Parametric equations of the lines are $\"\"$

and $\"\"$ .

Standard form of parametric equations of the line are $\"\"$ , where vector $\"\"$ is parallel line to the line.

Compare $\"\"$ with standard form.

Parallel line corresponding to the line $\"\"$ is $\"\"$ .

Consider $\"\"$ .

Similarly parallel line corresponding to the line $\"\"$ is $\"\"$ .

Consider $\"\"$ .

If these two parallel lines $\"\"$ are parallel, then the lines $\"\"$ and $\"\"$ also parallel.

The cross product of the two parallel lines is zero.

Find the cross product of $\"\"$ and $\"\"$ .

$\"\"$

Since the cross product is equal to zero, the two lines are parallel. \ \

The lines $\"\"$ and $\"\"$ are parallel lines. $\"\"$

The lines $\"\"$ and $\"\"$ are parallel lines.