# Math Help - 3D points on line?

1. ## 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!

2. 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.
$\overrightarrow {AB} = \left\langle {2,8, - 4} \right\rangle \;\& \,\overrightarrow {AC} = \left\langle { - 4, - 16,8} \right\rangle$.
Because, they are multiples of each other the points are colinear.

3. oh ok. That makes sense. thank you!
but out of curiosity... how would i do it with distances???

4. Im asking because this section is BEFORE the vectors section, so technically this solution shouldnt use vectors.

5. Originally Posted by collegestudent321
but out of curiosity... how would i do it with distances???
Find the distances $AB,~BC,~\&~AC$.
See if two of those add to the third.

6. Oh ok, cool... Easy enough. Thanks!