Step 1:

(a)

The two points are and .

The direction vector from the points and .

Required direction numbers as integers so, the direction vector multiplied with 3.

The direction vector .

The parametric equations passing through the point and parallel to the direction vector are

and .

Substitute and in parametric equations.

Parametric equations are and .

Step 2:

(b)

Symmetric equations:

If the direction numbers and are all non zero, then eliminate the parameter to obtain symmetric equations of the line.

.

Substitute and in symmetric equations.

.

Solution:

(a) Parametric equations are and .

(b) Symmetric equations are .