# Non colinear points

by esmeco
Tags: colinear, points
 P: 144 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 y2-y1=x2-x1 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!
 Sci Advisor HW Helper P: 3,031 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.
 P: 144 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 non-colinear, 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!
HW Helper
P: 3,031
Non colinear points

 Quote by esmeco 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 non-colinear, 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!
"Different than zero" would come in if you chose to use the cross product to test for colinearity, but not if you use the dot product. What must be true about the cross product of parallel vectors? How does the dot product depend on the angle between two vectors?
 P: 144 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?