- #1
natashajane
- 7
- 0
I've just had a brain block... how do I work out the distance between a point (-5,10,13) and a parametric equation:
x(t) = 57- 4t
y(t) = 75 + 5t
z(t) = -t
x(t) = 57- 4t
y(t) = 75 + 5t
z(t) = -t
ice109 said:he didn't ask for the minimum distance, he asked for the distance. hence the distance will be a function of t
The distance between a point and a parametric equation is the shortest distance between the point and any point on the curve described by the parametric equation.
The distance between a point and a parametric equation can be calculated using the formula d = √((x - xp)2 + (y - yp)2 + (z - zp)2), where (xp, yp, zp) is the coordinates of the point and (x, y, z) is any point on the parametric curve.
No, the distance between a point and a parametric equation is always a positive value. It represents the length of the shortest line segment connecting the point and the curve described by the parametric equation.
The parameter value affects the distance between a point and a parametric equation by determining the specific point on the parametric curve that is being evaluated. As the parameter value changes, the coordinates of the point on the curve change, and therefore the distance between the point and the curve may also change.
Finding the distance between a point and a parametric equation can be useful in many applications, such as in physics, engineering, and computer graphics. It allows us to determine the closest point on a curve to a given point, which can help in optimizing designs and solving real-world problems.