Equation of lines / planes (vectors)

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April 28th 2008, 11:10 AM
Somersault

Equation of lines / planes (vectors)

Hi,

I'm having trouble figuring out this problem -- i"m not sure if my approach is right (there is no answer key).

Quote:

Find the equation of the line normal to the plane 3x - 2y + z = 4 and containing the point (1, 2, -1)

Do I just use the normal vector from the plane <3, -2, 1>? Not really sure how to start this problem...
April 28th 2008, 11:48 AM
earboth

Quote:

Originally Posted by Somersault

Hi,

I'm having trouble figuring out this problem -- i"m not sure if my approach is right (there is no answer key).

Do I just use the normal vector from the plane <3, -2, 1>? Not really sure how to start this problem...

You are right: The direction vector of the line must be the same as the normal vector of the plane.

If $\vec r$ is the stationary vector of any point of the line the equation of the line becomes:

$l: \vec r= \langle 1, 2, -1 \rangle + t \cdot \langle 3, -2, 1 \rangle~,~t \in \mathbb{R}$
April 28th 2008, 02:55 PM
Somersault

Ah, yes. Thanks. I figured it out shortly after posting my question...