Linear Algebra(parametric equations)

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In summary: Whenever looking at the equation of a plane in the form ax + by + cz + d = 0, the vector (a,b,c) is always the vector that is perpendicular to the plane (which is a normal vector). Since you are trying to find the direction vector for a line perpendicular to the given plane, finding the direction vector is easy. You also have the point P, so you should be able to answer it now.I'd hoped you could look this up but, yes, a normal to ax+by+cz=constant is (a,b,c). For your homework, explain to me why.
  • #1
ur5pointos2sl
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The question states:
Determine the parametric equations of the line passing through the point P(2,1,0) and perpendicular to the plane 2x-5y=6.

The equation to obviously use is the "point-parallel" I'm guessing. X= P +tV where P is the point and V is a vector, and X=(x,y,z). But how would I use this since there isn't a vector given for V and instead is the plane 2x-5y=6? Maybe this isn't the one I need to use. Please help.
 
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  • #2
The direction vector for the line is the normal to the plane. Do you know how to find the normal to a plane?
 
  • #3
Dick said:
The direction vector for the line is the normal to the plane. Do you know how to find the normal to a plane?

n . (x - p) ?
 
  • #4
You can also write that as n.(x,y,z)=constant. What's a normal for your plane?
 
  • #5
Dick said:
You can also write that as n.(x,y,z)=constant. What's a normal for your plane?

hm I honestly have no idea how to do this problem. I could set it up like this but then what would I do next?

N . (( x,y,z) - (2,1,0)= 0

x-2
y-1
z-0 ?
 
  • #6
You don't need the point P to find the normal to the plane. Please look up how to find the normal to a plane ax+by+cz=constant.
 
  • #7
Dick said:
You don't need the point P to find the normal to the plane. Please look up how to find the normal to a plane ax+by+cz=constant.

Ok I am not really finding too much on the topic.. I did however find one thing that said you want to use the cross product to find the norm to the plane.
 
  • #8
would the norm happen to be (0,0,-4)
 
  • #9
No, one choice for the normal would be (2,-5,0). Now where did I get that?
 
  • #10
Dick said:
No, one choice for the normal would be (2,-5,0). Now where did I get that?

ahhh from the equation itself. so that would be the case everytime?
 
  • #11
ur5pointos2sl said:
ahhh from the equation itself. so that would be the case everytime?


Whenever looking at the equation of a plane in the form ax + by + cz + d = 0, the vector (a,b,c) is always the vector that is perpendicular to the plane (which is a normal vector). Since you are trying to find the direction vector for a line perpendicular to the given plane, finding the direction vector is easy. You also have the point P, so you should be able to answer it now.
 
  • #12
ur5pointos2sl said:
ahhh from the equation itself. so that would be the case everytime?

I'd hoped you could look this up but, yes, a normal to ax+by+cz=constant is (a,b,c). For your homework, explain to me why.
 

1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations, linear functions, and their representations in vector spaces. It involves the use of matrices and vectors to solve problems related to systems of linear equations.

2. What are parametric equations?

Parametric equations are a set of equations that express the coordinates of a point in terms of one or more parameters. They are often used to describe curves and surfaces in space.

3. How are parametric equations used in linear algebra?

Parametric equations are used in linear algebra to represent systems of linear equations in a more concise and efficient manner. They also allow for easier visualization of geometric objects and their transformations.

4. What are the advantages of using parametric equations in linear algebra?

Using parametric equations in linear algebra allows for a more flexible and powerful representation of geometric objects and their transformations. It also simplifies calculations and can lead to more efficient solutions.

5. What are some real-world applications of linear algebra and parametric equations?

Linear algebra and parametric equations have many real-world applications, including computer graphics, image processing, physics, and engineering. They are also used in economic analysis, data analysis, and machine learning algorithms.

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