Determining whether three points lie on a straight line in three dimensionby k1point618 Tags: determining, dimension, line, points, straight 

#1
Aug2608, 05:53 PM

P: 25

1. The problem statement, all variables and given/known data
Determine whether the points lie on straight line A(2, 4, 2) B(3, 7, 2) C(1, 3, 3) 2. Relevant equations 3. The attempt at a solution I've looked up at the equation for lines in three dimension, and it appears to be x=x_0+at y=y_0+bt z=z_0+ct i tried to take the x y z for A and B and try to solve for a, b, c. Then if the same a, b, c work for BC, then ABC is on a line. That is my thought, but i can't manage to do the first part. I don't know how to use the information given and the equations to start with... Anyone please help me with this. This is my first time working with 3dimensional coordinate system... 



#2
Aug2608, 06:11 PM

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You don't have to work all that hard to get the equation for the line. In vector form the equation is [x,y,z]=A+(BA)*t. Do you see why that gives you [x,y,z]=A at t=0 and [x,y,z]=B at t=1?? Can you translate that into equations for x, y and z?




#3
Aug2608, 06:19 PM

P: 25

But i'm still not sure about how to translate that in to equations for x, y and z. 



#4
Aug2608, 06:24 PM

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Determining whether three points lie on a straight line in three dimension
BA=[1,3,4], right? So you have [x,y,z]=[2,4,2]+[1,3,4]*t. I read off x=2+t. I just equated the first component of the two sides. What do you get for y and z?




#5
Aug2608, 07:27 PM

P: 25

i see...
so y= 4+3t and z=24t? and from here, i can use the x, y, z equation for points BC to see if it's a line? 



#6
Aug2608, 10:41 PM

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Nah, just see if C is on the line, you don't need another set of equations. If there is a t that solves all three, then it's on the line. If not, not.




#7
Aug2708, 02:52 PM

P: 25

Thank you very much. I've got it



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