Find symetric equations for the line of intersection of the planes

In summary, to find the symmetric equations for the line of intersection of two planes, one must first find the direction vector of the line by taking the cross product of the normal vectors of the two planes. Then, using a point on the line, the parametric equations can be determined. Finally, by substituting the parametric equations into the symmetric equations, the desired equations can be found.
  • #1
jdj333
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Homework Statement



Find symmetric equations for the line of intersection of the planes

Homework Equations



5x - 2y - 2z = 1

4x + y + z = 6

The Attempt at a Solution



I interpret this problem to say that I need to find a line of intersection of the two planes. I think I add them together and get 9x -y -z = 7.

After which, I need to find symmetric equations of that line and I think that is what I am having trouble with. I would like a little background into what a symmetric equation is. The book says that I need to first find a parametric equation then solve for t. Thanks!
 
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  • #2
jdj333 said:
I think I add them together and get 9x -y -z = 7.

That is not a line.

The book says that I need to first find a parametric equation then solve for t.

Exactly. See http://www.math.ucla.edu/~ronmiech/Calculus_Problems/32A/chap11/section5/716d13/716_13.html the answer to part (a) for an example.
 

FAQ: Find symetric equations for the line of intersection of the planes

What are symmetric equations?

Symmetric equations refer to a set of equations that describe a line or a plane in a way that is independent of the coordinate system used. They are often used in mathematics and physics to express geometric concepts in a general and concise manner.

How do you find symmetric equations for the line of intersection of two planes?

To find symmetric equations for the line of intersection of two planes, you can use the cross product of the normal vectors of the two planes. This will give you the direction vector of the line. Then, you can use the coordinates of a point on the line to create the symmetric equations using the direction vector.

Can you explain the concept of normal vectors in relation to symmetric equations?

Normal vectors are perpendicular to the planes they represent and can be used to determine the orientation and direction of the planes. In symmetric equations, the normal vectors of two planes are used to find the direction vector of the line of intersection, which is then used to create the equations.

Are symmetric equations unique for every line of intersection?

Yes, symmetric equations are unique for every line of intersection. This is because the direction vector of the line is determined by the normal vectors of the two planes, which are unique for each plane. Therefore, the equations will be different for every pair of planes.

Can symmetric equations be used to find the point of intersection of two planes?

No, symmetric equations cannot be used to find the point of intersection of two planes. These equations only describe the direction vector of the line of intersection, not the specific points on the line. To find the point of intersection, you would need to solve the equations of the two planes simultaneously.

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