At least three points P_1, P_2, P_3, ..., are said to be collinear in the event that they lie on a solitary straight line L. A line on which focuses lie, particularly in the event that it is identified with a geometric figure, for example, a triangle, is in some cases called a hub.
Further Explanation:
Data:
Two are inconsequentially collinear since two decide a line.
Three x_i=(x_i,y_i,z_i) for i=1, 2, 3 are collinear iff the proportions of separations fulfill
x_2-x_1:y_2-y_1:z_2-z_1=x_3-x_1:y_3-y_1:z_3-z_1.
(1) solution:
A somewhat progressively tractable condition is gotten by taking note of that the territory of a triangle controlled by three will be zero iff they are collinear (counting the ruffian instances of two or each of the three being simultaneous),
(2) Sol.
or on the other hand, in extended structure,
x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0.
(3) Answer:
This can likewise be written in vector structure as
Tr(xxy)=0,
(4) example
where Tr(A) is the aggregate of parts, x=(x_1,x_2,x_3), and y=(y_1,y_2,y_3).
The condition for three x_1, x_2, and x_3 to be collinear can likewise be communicated as the explanation that the separation between any one point and the line dictated by the other two is zero. In three measurements, this implies setting d=0 in the point-line separation
d=(|(x_2-x_1)x(x_3-x_1)|)/(|x_2-x_1|),
(5) basically
giving basically
|(x_2-x_1)x(x_1-x_3)|=0,
Answer Details:
Subject: Mathematics
Level: High School.
Key Words:
(1) solution:
(2) Sol.
(3) Answer:
(4) example
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