# How do you find parametric equations for the line through the point (0,1,2) that is perpendicular to the line x =1 + t , y = 1 – t , z = 2t and intersects this line?

##### 2 Answers

See below.

#### Explanation:

Given the line

where

The elements

The sought line

Please see the helpful video and the explanation for my solution to the problem.

#### Explanation:

Here is a video that helped me to know how to do this problem. Helpful Video

Lets write the vector equation of the line:

A plane that is perpendicular to this line will have the general equation:

We make it contain the point by substituting in the point and solving for c:

The plane

To find the point where the line intersects the plane, substitute the parametric equations of the line into the equation of the plane:

The line intersects the plane at the point (3/2, 1/2, 1)

check

This checks.

The vector,

The vector equation of the line is:

The parametric equations are: