Hi,

How do I find the vector equation of this.

given the line travels through point (1,0,6) and perpendicular to the plane x+3y+z=5

I'm guessing here by do I do something like this

(x-1)+(y-0)+(z-6) = x+3y+z-5 ? ??(Headbang)

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- June 7th 2008, 08:34 PMCrakavector equation of line through point perpendicular to plane
Hi,

How do I find the vector equation of this.

given the line travels through point (1,0,6) and perpendicular to the plane x+3y+z=5

I'm guessing here by do I do something like this

(x-1)+(y-0)+(z-6) = x+3y+z-5 ? ??(Headbang) - June 7th 2008, 08:43 PMTheEmptySet
- June 7th 2008, 08:44 PMJhevon
the direction vector of the line is the normal vector to the plane. so we have a line passing through (1,0,6) in the direction <1,3,1>. how would you write the equation for this line?

You know why the normal vector of the plane is the direction vector of the line, right?

EDIT: well, if i'm going to be beaten by anyone, it might as well be TES... you mind me calling you TES, TheEmptySet? - June 7th 2008, 08:44 PMearboth
- June 7th 2008, 08:45 PMo_O
Given a line of the form , the vector is perpendicular to the line. This is the vector component that is parallel to your line, i.e. the of the vector equation: . You have a point on the line and thus you can find to complete your equation.

EDIT: WOW BEaTEN BY 3 PEOPLE???? - June 7th 2008, 08:49 PMTheEmptySet
- June 7th 2008, 09:00 PMCrakaQuote:

Quote:

Originally Posted by**Craka**http://www.mathhelpforum.com/math-he...s/viewpost.gif

*Hi,*

How do I find the vector equation of this.

given the line travels through point (1,0,6) and perpendicular to the plane x+3y+z=5

I'm guessing here by do I do something like this

(x-1)+(y-0)+(z-6) = x+3y+z-5 ? ??(Headbang)

The Normal Vector to the plane is http://www.mathhelpforum.com/math-he...a93880f4-1.gif You can get this by taking the gradient of the plane.

To find the vector equation of the plane

http://www.mathhelpforum.com/math-he...069ae4df-1.gif

so we get

http://www.mathhelpforum.com/math-he...eead6920-1.gif

sorry didn't realise needed to use the equation of that format. Obviously if there were a j component that would be included in (i+6k) ? - June 7th 2008, 09:08 PMo_O
Given the plane , the vector is orthogonal to the plane.

The j component is present as 0j. - June 7th 2008, 09:09 PMTheEmptySet
Yes it would need to be included. The notation I used is what I am used to. There are many other ways this could have been written for example

Then the equation of the line would be

They also could have been written in parametric form.

So I would use whatever form your professor or book uses. (Clapping)