$\"\"$

\

The parametric equations of a line:

\

The initial point on the line is $\"\"$ and is perpendicular to the line $\"\"$ then the parametric equations are $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

(a)

\

The line passing through the point is $\"\"$ and is perpendicular to the line $\"\"$ .

\

Here $\"\"$ and $\"\"$ .

\

Substitute the corresponding values in $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Therefore, the parametric equations are $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

The parametric equations are $\"\"$ , $\"\"$ and $\"\"$ .

\

(b)

\

Find the intersection points of the coordinate planes.

\

For the intersection of $\"\"$ -plane set $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ , $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Therefore, the point of intersection with $\"\"$ -plane is $\"\"$ .

\

$\"\"$

\

Find the intersection point of $\"\"$ -plane, set $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ , $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Therefore, the point of intersection with $\"\"$ -plane is $\"\"$ . $\"\"$

\

Find the intersection point of $\"\"$ -plane, set $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ , $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Therefore, the point of intersection with $\"\"$ -plane is $\"\"$ .

\

$\"\"$

\

(a) The parametric equations are $\"\"$ , $\"\"$ and $\"\"$ .

\

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