Three points X = (3, 0, 1) Y = (4, 5, 0) Z = (−3, −8, −1)
Are they collinear?

Question

Three points X = (3, 0, 1) Y = (4, 5, 0) Z = (−3, −8, −1) 
Are they collinear?

ganeshie8 · Answer

what do you know about cross product of two vectors ?

anonymous · Answer

Collinear points have same slope

anonymous · Answer

Can u find the points of them

mayankdevnani · Answer

@hopelovelift  do you know the property of collinear points ?

anonymous · Answer

I mean slope

ganeshie8 · Answer

interesting, how can we find slope in 3 dimensions ?

mayankdevnani · Answer

yeah,too interesting

anonymous · Answer

Okay i'll show my working.
So to find line/vector I did this XY= Y-X and YZ=Z-Y
Keep in mind that I gave you points not three vectors :P
Then I assumed that Collinear points are Parallel.
XY=kYZ
Then I found out that it is not parallel therefore not collinear.

mayankdevnani · Answer

@Raja99  can you tell me how to find slope in 3 dimensions?

anonymous · Answer

points wont be parallel.. online lines

anonymous · Answer

only*

anonymous · Answer

Also I have another equation if you guys don't mind. 
 Let A = (2, 1, 3) and B = (−1, −1, −1). Find the vector parametric equation of the line through
A and B. Using your equation determine a point C, distinct from A and B such that A, B, C are
collinear.
I Just want to know how to solve it because I missed the lectures on parametric equation...

mayankdevnani · Answer

@hopelovelift  i tell you a shortcut.

Shortcut:- Find discriminant of all the points and equate to zero.

Because AREA OF COLLINEAR POINTS IS ZERO.
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anonymous · Answer

no idea.. but can we look in 2d like xy..xz..yz

anonymous · Answer

What is the graph showing? Are you telling me its collinear or not?

mayankdevnani · Answer

see,if area of all the points become zero,then we can definitely say that these points are collinear and if they don't get zero,so they are not collinear points.

And to find area ,use discriminant.

mayankdevnani · Answer

understood? @hopelovelift

anonymous · Answer

Okay thanks.

mayankdevnani · Answer

welcome :)

anonymous · Answer

Do you also know how to solve the question above?

mayankdevnani · Answer

use discriminant,i said above

anonymous · Answer

To find the parametric equation?

mayankdevnani · Answer

no....

mayankdevnani · Answer

attachment

mayankdevnani · Answer

https://www.youtube.com/watch?v=21LWuY8i6Hw this will help you so much.... Using this method,if this is equal to 0,then these are collinear points

anonymous · Answer

Okay thanks

mayankdevnani · Answer

welcome :)