Finding A and L in Parametric Equation X(t)

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In summary, the parametric equation X(t)=A+tL represents a line passing through point P with coordinates (2,-3,1). The parameter t represents distance from point P, with positive values indicating the direction of the I component of L. The line is orthogonal to the plane with the equation 4x-6y+5z=6. To solve for A and L in vector component form, t must be understood as a number and L as the slope of the line.
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Amebos
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Homework Statement


The equation X(t)=A+tL is the parametric equation of a line through the point P:(2,-3,1). The parameter t represents distance from point P, directed so that the I component of L is positive. We know that the line is orthogonal to the plane with the equation 4x-6y+5z=6. Then solve for A and L in vector component form.


Homework Equations



Standard Vector Calculus equations.

The Attempt at a Solution



My problem here is simply understanding what the problem is saying. The t term is throwing me off. Hopefully some of you could shed some light on this.
 
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  • #2
t is a number - like x in the 2d straight line equation y=m*x+b. L is analogous to the slope m. So as t runs from -infinity to infinity X(t) runs through a curve of points. That curve is a straight line.
 

What is a parametric equation?

A parametric equation is a mathematical representation of a set of coordinates in terms of one or more independent variables, usually denoted as "t". It allows for the visualization of complex curves and surfaces.

Why is it important to find "A" and "L" in a parametric equation?

By finding the values of "A" and "L" in a parametric equation, we can determine the amplitude and wavelength of the curve or surface being represented. This information is crucial in understanding the behavior and characteristics of the equation.

How do you solve for "A" and "L" in a parametric equation?

To solve for "A" and "L", we can use the standard form of a parametric equation which is x(t) = A*cos(L*t) and y(t) = A*sin(L*t). We can then compare this form to the given parametric equation and solve for "A" and "L" using algebraic techniques.

What is the significance of "t" in a parametric equation?

"t" is the independent variable in a parametric equation, meaning that it is not affected by the other variables in the equation. It represents the parameter or input that determines the values of x and y coordinates in the equation.

How can finding "A" and "L" be applied in real-life situations?

Parametric equations are used in various fields such as physics, engineering, and computer graphics. Finding "A" and "L" can help in modeling and predicting the behavior of physical systems, designing structures and machines, and creating 3D animations and simulations.

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