# Plotting points in three-dimensional space

• ChiralSuperfields
In summary, Four points are given, three of which are plotted in 3D space, and the fourth is plotted in 2D space. The order and relative spacing of ##P', Q', R'##, and ##S'## are the same as those of ##P, Q, R## and ##S##.
ChiralSuperfields
Homework Statement
Relevant Equations
For this problem,
,
The four points are,
##P(8,2,6)##
##R(-2,16,-2)##
##Q(3.9,2)##
##S(\frac{14}{3}, \frac{20}{3}, \frac{10}{3})##

And the solution is,

However, does someone please know what in the proportion 2:1:3 mean?

Many thanks!

ChiralSuperfields said:
However, does someone please know what in the proportion 2:1:3 mean?

ChiralSuperfields
renormalize said:

I guess I can see where the comes from if we use a ruler to find the ratio.

However, how dose one know that without the drawing?

Many thanks!

ChiralSuperfields said:
However, how dose one know that without the drawing?
You are given the ##(x,y,z)## coordinates of each of the 4 points ##P,Q,R,S##. Can you can plot them in 3D space to see where they fall along the line? Do you know how to subtract two vectors to get their difference vector? And can you calculate the length of the difference vector to get the distance between the tips of those two vectors? (P.S.: "does" not "dose".)

scottdave and ChiralSuperfields
renormalize said:
You are given the ##(x,y,z)## coordinates of each of the 4 points ##P,Q,R,S##. Can you can plot them in 3D space to see where they fall along the line? Do you know how to subtract two vectors to get their difference vector? And can you calculate the length of the difference vector to get the distance between the tips of those two vectors? (P.S.: "does" not "dose".)

True it would be hard to tell which points are in which order if we did not graph the points in 3D space. Oh I now see. So if we find the magnitude of the difference vector between adjacent points then we should be able to find the ratio between them.

Many thanks!

scottdave and renormalize
ChiralSuperfields said:
True it would be hard to tell which points are in which order if we did not graph the points in 3D space. Oh I now see. So if we find the magnitude of the difference vector between adjacent points then we should be able to find the ratio between them.
To help get the ordering, you can also find the distances between pairs of non-adjacent points. For example, the pair of points with the biggest distance between them must be at the ends.

To simplify the arithmetic, a 'trick' you could use is to change all coordinate-scales by a factor of 3 to get rid of the thirds.
##S' = (3*\frac{14}{3}, 3*\frac{20}{3}, 3*\frac{10}{3}) = (14, 20, 10)##
##P' = (3*8,3*2,3*6) = (24, 6, 18)##
etc.

The order and relative spacing of ##P', Q', R'##, and ##S'## are the same as those of ##P, Q, R## and ##S##. But you don't have to work with the messy thirds. (But if you are not completely clear why that works, stick to using thirds.)

EDIT. A simpler way to get the order is to find how far each point is from the origin.
That won't always work, so struck-through.

Last edited:
ChiralSuperfields
ChiralSuperfields said:
However, how dose one know that without the drawing?

ChiralSuperfields, SammyS and Steve4Physics
I had fun plotting things -- and, being lazy, realized a 3D plot isn't necessary: 2D, e.g. the projection on the XY plane, is already enough:

##\ ##

ChiralSuperfields and Steve4Physics
BvU said:
I had fun plotting things -- and, being lazy, realized a 3D plot isn't necessary: 2D, e.g. the projection on the XY plane, is already enough
In fact 1D is enough! Only the x-coordinates are required to answer the question. (Or alternatively, only the y or only the z ones.)

ChiralSuperfields and BvU

• Precalculus Mathematics Homework Help
Replies
8
Views
540
• Precalculus Mathematics Homework Help
Replies
6
Views
940
• MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
103
• Precalculus Mathematics Homework Help
Replies
7
Views
2K
• Precalculus Mathematics Homework Help
Replies
7
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
745
• Precalculus Mathematics Homework Help
Replies
11
Views
1K
• Precalculus Mathematics Homework Help
Replies
45
Views
4K
• Introductory Physics Homework Help
Replies
6
Views
164
• Introductory Physics Homework Help
Replies
6
Views
699