SMA_01 said:@LCKurtz: Yeah I used the old method of finding the parametric equations, taking PQ as the vector, and using either P or Q as points. That didn't work out. I actually figured out how to do it, I just want to understand it. Like geometrically, what is the question saying?
SMA_01 said:@HallsofIvy and LCKurtz: Thanks, so basically I'm re-scaling the original linear equations to fit into the new parameters? Sorry, I'm just trying to understand the geometrical aspect.
A vector parametric equation is a way to represent a line or curve in three-dimensional space using parameters. It is typically written in the form of r(t) = ai + bj + ck, where i, j, and k are unit vectors and a, b, and c are constants that determine the direction and position of the line or curve.
A vector parametric equation is useful for representing and visualizing complex curves and surfaces, as well as for solving problems in physics, engineering, and other fields that involve motion or direction in three-dimensional space.
To find a vector parametric equation through a set of given points, you first need to determine the direction vector by subtracting the coordinates of one point from the coordinates of another point. Then, you can use the direction vector and one of the given points to create the parametric equation by plugging in the values for a, b, and c.
No, you cannot use any two points to find a vector parametric equation. The points must be distinct and not lie on the same line or curve. Otherwise, the direction vector would be zero and the equation would not accurately represent the desired line or curve.
Yes, there are alternative ways to represent a line or curve in three-dimensional space, such as using a scalar parametric equation, a symmetric parametric equation, or a Cartesian equation. Each of these methods has its own advantages and may be more suitable for certain applications.