- #1
tandoorichicken
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How do you find the equation of a line between two points in three dimensional space? I sort of forgot. =\
0rthodontist said:c(t) = (P-Q)t+P
d_leet said:Shouldn't that be c(t) = (P-Q)t+Q
because at t = 0 you should get Q, and at t = 1 you should get P which isn't what happens in your equation.
The equation of a 3D line is a mathematical representation that describes the relationship between the x, y, and z coordinates of points that lie on that line.
At least two points are needed to find the equation of a 3D line. These two points must lie on the line and have distinct x, y, and z coordinates.
No, the equation of a 3D line cannot be found if the points are on the same plane. A line on a plane can be represented by a different equation, such as a parametric equation.
The steps for finding the equation of a 3D line from two points are:
1. Find the slope of the line using the two points
2. Choose one point and use the slope to write the equation in point-slope form
3. Rewrite the equation in general form by distributing and rearranging terms
4. Simplify the equation and write it in standard form to get the final equation.
Yes, the equation of a 3D line can be used to find the distance between two points on that line. Once the equation is found, the distance formula can be used to calculate the distance between the two points.