# Find equation of plane passing through a point, perpendicular to a line

• Mar 12th 2013, 05:27 AM
johnstobbart
Find equation of plane passing through a point, perpendicular to a line
Good day,

Here is my current problem:

Find the equation of the plane that passes through the point (-2, 3, 4) and is perpendicular to the line passing through the points (4, -2, 5) and (0, 2, 4).

My attempt

Well, I need a vector, which I obtained from the two given points. I get: (-4, 4, -1).
Now, from my understanding, the point on the plane is perpendicular to this point, so I can form the general equation with them:

Equation of plane:
(-4, 4, -1).(x + 2, y - 3, z - 4) = 0
When simplifed to its general form, I get:
-4x + 4y - z = 16

I think that I'm doing it correctly, however, I also feel as though I should be using the cross product. Can anyone point me in the right direction?
• Mar 12th 2013, 06:27 AM
Plato
Re: Find equation of plane passing through a point, perpendicular to a line
Quote:

Originally Posted by johnstobbart
Here is my current problem:
Find the equation of the plane that passes through the point (-2, 3, 4) and is perpendicular to the line passing through the points (4, -2, 5) and (0, 2, 4).

My attempt
Well, I need a vector, which I obtained from the two given points. I get: (-4, 4, -1).
Now, from my understanding, the point on the plane is perpendicular to this point, so I can form the general equation with them:
Equation of plane:
(-4, 4, -1).(x + 2, y - 3, z - 4) = 0
When simplifed to its general form, I get:
-4x + 4y - z = 16

You are correct.
• Mar 13th 2013, 07:29 AM
johnstobbart
Re: Find equation of plane passing through a point, perpendicular to a line
Quote:

Originally Posted by Plato
You are correct.

Thank you very much for your help