Equation of a line from Parametric equations

In summary, the conversation is about finding the equation of a line from parametric equations. The person mentions using a formula like x-1/a = y-1/b = z-1/c, but is unsure of what to do next. Another formula is mentioned, <x_0,y_0,z_0>+ t<a,b,c>, but the person is still confused. The conversation then shifts to finding the equation of a plane containing the line and a given point. The person wonders if they can use the second half of the previously mentioned formula to find the N vector needed for the equation of the plane.
  • #1
Spectre32
136
0
How does one find the equation of a line from parametric equations?

In spefiic I'm looking at this: x(t) = 1+2t , y(t) = -1 + 3t , z(t) = 4+t... I think i got to use something liek x-1/a = y-1/b=z-1/c or something like that. If what i just said is true, then I'm lost on what to do next.


Thanks
 
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  • #2
t = (x-1)/2 = (y+1)/3 = z-4
 
  • #3
or wait... do i uses this:

<x_0,y_0,z_0>+ t<a,b,c> ...


now I'm really confused.
 
  • #4
Yeah tide, i did that, but then isn't there something else i got to do? I don't know I'm kinda confused about this stuff. Also allow me to add the rest of the question. IT's find the equation of a plane containing that line, and the point (1,-1,5). Sooo i need the N =<a,b,c> vector and a point ot get my equation of a plane.. So could i use use the second half of that equation i posted aboce ( t<a,b,c>) to get what i need for my N vector?
 
Last edited:

What is the equation of a line from parametric equations?

The equation of a line from parametric equations is a mathematical representation of a line using two independent variables, usually denoted as t and s. It is expressed as x = x(t) and y = y(t), where x and y represent the coordinates on the line at a specific value of t.

How do you convert parametric equations to the equation of a line?

To convert parametric equations to the equation of a line, you can eliminate the parameter t by solving for it in one of the equations and substituting that value into the other equation. This will result in an equation in terms of x and y, which represents the equation of the line.

What is the significance of the parameter t in parametric equations?

The parameter t in parametric equations represents the independent variable, which determines the values of x and y on the line. By varying the value of t, you can trace out the entire line and visualize its shape and direction.

Can parametric equations represent any type of line?

Yes, parametric equations can represent any type of line, including straight lines, curved lines, and even vertical and horizontal lines. By manipulating the equations, you can adjust the slope, intercept, and curvature of the line.

How are parametric equations used in real-world applications?

Parametric equations have various applications in fields such as physics, engineering, and computer graphics. They are commonly used to represent the motion of objects, such as projectiles, and to model complex curves and shapes. They are also used in computer programming to create animations and simulations.

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