# Equations of a plane with vector form

• Sep 30th 2008, 08:16 AM
GreenMachine
Equations of a plane with vector form
Hi, I have an exam tomorrow and never learned vector form, but it is showing up constantly on this review.

What is the equation of the plane containing (1,1,1) and the line r= <1,0,-1> + t <1,0,1>?

Could someone explain to me what the equation of that vector actually means, and how would I go about solving this problem?

Thank you!
• Sep 30th 2008, 08:28 AM
bobak
let a be a point on the plane let n be the vector that is perpendicular to the plane and let r be any point on the plane. the vector going from a to r is a direction vector and is perpendicular to the normal as it lies in the plane. therefore (r-a).n = 0 and this can be written as r.n = a.n . that is how you write the equation of a plane in vector form.

You are given a point on the plane, so all you need to do now is find a vector perpendicular to it. the normal will be perpendicular to the direction of the line (1 , 0 , 1) and then vector going form (1 , 0 , -1 ) to ( 1, 1, 1). you need to find a vector perpendicular to both (1 , 0 , 1) and (0 , - 1 , - 2). to find the vector take the cross product of the two vectors.

Bobak
• Sep 30th 2008, 08:38 AM
GreenMachine
Okay, I understand the part about how to find the equation of the plane. Thank you very much.

But, where does the t come from in that vector form? And why is it added...I guess I don't understand that very much.
• Sep 30th 2008, 08:59 AM
bobak
Quote:

Originally Posted by GreenMachine
Okay, I understand the part about how to find the equation of the plane. Thank you very much.

But, where does the t come from in that vector form? And why is it added...I guess I don't understand that very much.

r= <1,0,-1> + t <1,0,1> is the equation of a vector line that pass through the point <1,0,-1> in the direction of the vector <1,0,1>. t is just a scalar parameter that can be any real number.

Look at the diagram here for a better idea

Bobak
• Sep 30th 2008, 09:01 AM
GreenMachine
Okay. Thank you. That makes much more sense of how that describes a line. Thanks.