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Non colinear points 
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#1
Dec1906, 03:44 PM

P: 145

1. The problem statement, all variables and given/known data
The problem states the following: Show that the points of space A(3,1,5) B(8,3,3) and C(2,1,4) are not colinear 2. Relevant equations I've tried to use the equation y2y1=x2x1 for the straight line on IR2 but since we are working in IR3 the same formula doesn't apply 3. The attempt at a solution I'm not sure how we calculate the slope of the straight line on IR3 or if there's another formula to demonstrate that the points are non colinear. Thanks in advance for the reply! 


#2
Dec1906, 03:51 PM

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P: 3,033

You could create displacement vectors from one of the points to the other two and take the dot product or cross product of the two vectors. Either way, if you know how the dot and cross products of parallel vectors behave, you can reach the needed conclusion from either one of these products.



#3
Dec1906, 10:20 PM

P: 145

Let me see if I understood this correctly...I should make 2 vectors out of these 3 points,lets say vector AB and vector BC.To demonstrate that the points are noncolinear, calculating the dot or cross product they must be different than zero.If vector AB and vector BC are not multiple of one another(hence not parallel), the vectors are non colinear,hence the points are non colinear.Am I right on this?Feel free to correct me if I'm wrong!Thanks in advance for the reply!



#4
Dec1906, 10:58 PM

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Non colinear points



#5
Dec2006, 07:37 AM

P: 145

After searching a bit, I think I'm correct now(but again feel free to correct me if I'm wrong): The cross product of vectors must be zero,hence if it's zero their parallel,and since their parallel their colinear.Using the dot product, if the result of that product equals one, the vectors are parallel.
Am I right? 


#6
Dec2006, 09:00 AM

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P: 3,033

Another way to show that your points are colinear is to show that one vector is a multiple of the other. If you compare the ratios of corresponding components, all the ratios will be the same if the points are colinear. 


#7
Dec2006, 09:17 AM

P: 145

Thank you for your help!I now understand it!



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