Find Slope of Points in Space?

Question

How do I find the slope between 2 points in space?

Sample:

Find the slope between point R(3, 7, 8) and S(3, 5, 9)?

Answer 1

You can find the distance between two points in space
d^2=(3-3)^2+(7-5)^2+(8-9)^2
d^2= 0+4+1=5

d=sqrt(5)

slope is tanx between the line and x axis in positive direction in plane.
no slope in space.

Answer 2

to find the equation of the line in 3D, you do not need to find a slope.

Instead, compute the directional vector: S-R = (3-3, 5-7,9-8) = (0,-2,1)

Now, pick any point on the line, e.g. R

your equation of the line becomes (3, 7, 8) + (0,-2,1)t where t is a constant.

**A line in R^n through x in R^n with direction v is defined by x+vt.** Think of of the vector as the direction of your line. If v is extended indefinitely, it will eventually hit all points on the line.

As a final note, notice that slope is defined as a ratio between two variables, but in R^3 we have more than 1 paring of variables.

Answer 3

Well, in this case, since the x-value is same on both points, then its (9-8)/(5-7) = -1/2. Or 1/2 depending on your prespective.