# 3D points on line?

• Aug 26th 2009, 11:39 AM
collegestudent321
3D points on line?
Hi guys, i have a question which seemed simple when i first read it but now i see for some reason i can't figure it out...

i have three 3D points: A(5,1,3) B(7,9,-1) and C(1,-15,11)

How can i determine if they are in a straight line?

I think it has something to do with finding the distances between the points but after that I dont know what i'm doing. Any help would be appreciated. thank you!
• Aug 26th 2009, 11:51 AM
Plato
Quote:

Originally Posted by collegestudent321
i have three 3D points: A(5,1,3) B(7,9,-1) and C(1,-15,11)
How can i determine if they are in a straight line?

There are several ways to proceed. Distance is one of them.
However, I would use vectors.
$\displaystyle \overrightarrow {AB} = \left\langle {2,8, - 4} \right\rangle \;\& \,\overrightarrow {AC} = \left\langle { - 4, - 16,8} \right\rangle$.
Because, they are multiples of each other the points are colinear.
• Aug 26th 2009, 11:53 AM
collegestudent321
oh ok. That makes sense. thank you!
but out of curiosity... how would i do it with distances???
• Aug 26th 2009, 11:55 AM
collegestudent321
Im asking because this section is BEFORE the vectors section, so technically this solution shouldnt use vectors.
• Aug 26th 2009, 12:12 PM
Plato
Quote:

Originally Posted by collegestudent321
but out of curiosity... how would i do it with distances???

Find the distances $\displaystyle AB,~BC,~\&~AC$.
See if two of those add to the third.
• Aug 26th 2009, 12:15 PM
collegestudent321
Oh ok, cool... Easy enough. Thanks!