The symmetric form of a line:

The initial point on the line is and is parallel to the vector then the symmetric form of a line equation is .

(a)

The line passes through the point is and is parallel to the vector .

Here and .

Substitute the corresponding values in .

Therefore, the symmetric form of a line is .

The symmetric form of a line is .

(b)

Find the intersects the coordinate planes.

For the intersection of -plane set .

Substitute in .

  and .

and

and .

Therefore, the point of intersection with -plane is .

Find  the intersection of -plane, set .

Substitute in .

  and .

and

and

and

Therefore, the point of intersection with -plane is .

Find  the intersection of -plane, set .

Substitute in .

  and .

and

and .

Therefore, the point of intersection with -plane is .

(a) The symmetric form of a line is .

(b) The intersection points of the coordinate planes is , and .