Question

what is the mean of collinear​

Answer 1

draw a line and as we know that line is a collection of points

or add some other points by yourself on that line then all those points will be called collinear

in the most simple words collinear are the points which lie on the same line.

Khushi here✔️✌

Answer 2

Answer:

COLLINEAR

Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a geometric figure such as a triangle, is sometimes called an axis.

Two points are trivially collinear since two points determine a line.

Three points x_i=(x_i,y_i,z_i) for i=1, 2, 3 are collinear iff the ratios of distances satisfy

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)

A slightly more tractable condition is obtained by noting that the area of a triangle determined by three points will be zero iff they are collinear (including the degenerate cases of two or all three points being concurrent), i.e.,

|x_1 y_1 1; x_2 y_2 1; x_3 y_3 1|=0

(2)

or, in expanded form,

x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0.

(3)

This can also be written in vector form as

Tr(xxy)=0,

(4)

where Tr(A) is the sum of components, x=(x_1,x_2,x_3), and y=(y_1,y_2,y_3).

The condition for three points x_1, x_2, and x_3 to be collinear can also be expressed as the statement that the distance between any one point and the line determined by the other two is zero. In three dimensions, this means setting d=0 in the point-line distance

d=(|(x_2-x_1)x(x_3-x_1)|)/(|x_2-x_1|),

(5)

giving simply

|(x_2-x_1)x(x_1-x_3)|=0,

(6)

where x denotes the cross product.

Since three points are collinear if x_3=x_1+c(x_2-x_1) for some constant c