Parametric equations and symmetric equations

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  • #1
maff is tuff
65
1

Homework Statement



Find parametric equations and symmetric equations for the line through the points (0,1/2,1) and (2,1,-3)



Homework Equations





The Attempt at a Solution



I started out graphing the points and connecting them with a straight line. I called the first point P and second Q. So the vector PQ = <2,1/2,-4>. So my vector r_0 is <0,1/2,1> so vector r = r_0 + tv

so <x,y,z>=<0,1/2,1> +t<2,1/2,-4>

<x,y,z> = <0+2t, 1/2 + t/2, 1-4t>

So my parametric equations are:

x=2t
y=1/2 + t/2
z=1-4t

And my symmetric eqs. are:

x/2 = 2y-1 = (z-1)/-4

This answer is wrong and I've done it a few times any hints? Thanks
 
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  • #2
maff is tuff said:

Homework Statement



Find parametric equations and symmetric equations for the line through the points (0,1/2,1) and (2,1,-3)



Homework Equations





The Attempt at a Solution



I started out graphing the points and connecting them with a straight line. I called the first point P and second Q. So the vector PQ = <2,1/2,-4>. So my vector r_0 is <0,1/2,1> so vector r = r_0 + tv

so <x,y,z>=<0,1/2,1> +t<2,1/2,-4>

<x,y,z> = <0+2t, 1/2 + t/2, 1-4t>

So my parametric equations are:

x=2t
y=1/2 + t/2
z=1-4t
Looks good. This is what I get, too.
maff is tuff said:
And my symmetric eqs. are:

x/2 = 2y-1 = (z-1)/-4
Instead of 2y - 1, write the expression in the middle as (y - 1/2)/(1/2). This is equal to what you have, but if your work is being computer-graded, it might not be smart enough to recognize different forms of the same thing.
maff is tuff said:
This answer is wrong and I've done it a few times any hints? Thanks
 
  • #3
It is not online homework. My paper actually says what you said to put but I found it easier to type so I multiplied by 2. So what do you think is wrong? Or is it right and there are multiple answers? Thanks.
 
  • #4
What you have is also correct, because 2y - 1 = (y - 1/2)/(1/2). If you multiply the expression on the right by 2/2, you get the expression on the left.
 
  • #5
maff is tuff said:

Homework Statement



Find parametric equations and symmetric equations for the line through the points (0,1/2,1) and (2,1,-3)



Homework Equations





The Attempt at a Solution



I started out graphing the points and connecting them with a straight line. I called the first point P and second Q. So the vector PQ = <2,1/2,-4>. So my vector r_0 is <0,1/2,1> so vector r = r_0 + tv

so <x,y,z>=<0,1/2,1> +t<2,1/2,-4>

<x,y,z> = <0+2t, 1/2 + t/2, 1-4t>

So my parametric equations are:

x=2t
y=1/2 + t/2
z=1-4t

And my symmetric eqs. are:

x/2 = 2y-1 = (z-1)/-4

This answer is wrong and I've done it a few times any hints? Thanks

Form a vector between the points:

say : B-A= <2, 0.5, -4 >

<x,y,z> - <2,1,-3> = k < 2, 0.5,-4>

and so on...
 
  • #6
stallionx said:
Form a vector between the points:

say : B-A= <2, 0.5, -4 >

<x,y,z> - <2,1,-3> = k < 2, 0.5,-4>

and so on...
stallionx, if you had read the thread before posting, you would have discovered that the OP had already arrived at the solution.
 

1. What are parametric equations?

Parametric equations are a set of equations that define the coordinates of a point in terms of one or more parameters. They are commonly used to describe curves and surfaces in mathematics and physics.

2. How are parametric equations different from Cartesian equations?

Parametric equations use parameters to define the coordinates of a point, while Cartesian equations use variables. Parametric equations are often used when dealing with curves and surfaces, while Cartesian equations are used for lines and planes.

3. What are symmetric equations?

Symmetric equations are a set of equations that describe a geometric figure using equations that are symmetric in terms of x, y, and/or z. They are often used to describe geometric shapes such as lines, planes, and spheres.

4. How are parametric equations and symmetric equations related?

Parametric equations and symmetric equations are related because they both describe geometric figures in three-dimensional space. In some cases, parametric equations can be converted into symmetric equations and vice versa.

5. What is the importance of parametric and symmetric equations in science?

Parametric and symmetric equations are important in science because they allow us to describe and analyze complex shapes and curves in three-dimensional space. They are used in fields such as physics, engineering, and computer graphics to model and understand various phenomena and structures.

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