Step 1:

(a)

The parallel vector is .

The direction vector is .

The point is .

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.

The symmetric equations are .

Solution:

(a) Parametric equations are and .

(b) Symmetric equations are . \ \

Direction numbers as integers: and . \ \