If two vectors are collinear, why is x1y2-x2y1 equal to zero?

If two vectors are collinear, why is x1y2-x2y1 equal to zero?

If two vectors are collinear, then the two vectors are in a straight line or parallel to each other
So X1 / Y1 = x2 / Y2
Therefore, it is necessary to move items from left to right
X1yZ－X2y1＝0

Why do coordinates mean that two vectors are parallel x1y2-x2y1 = 0

If the two vectors are parallel, there must exist between the coordinates: X1 / x2 = Y1 / Y2, and then we can get x1y2-x2y1 = 0 by staggered expansion

Triangle plane vector
The relationship between the triangle ABC and the internal point m is vector Ma + vector MB + vector MC = vector 0. Is this point a special point of the triangle? In addition to the center of gravity, the outer center, the inner center and the perpendicular center of the triangle, what else is the center?

[arrow, dot, multiplication sign omitted]
Analysis: make the standard diagram, and preliminarily determine that the point is the center of gravity of the triangle
Let the midpoint of line AB be o, then OA + ob = 0 (...) (vector)
From the meaning of the title, (Mo + OA) + (Mo + OB) + (Mo + OC) = 0
That is 3Mo + OC = 0, so om = - OC / 3
According to the theorem of center of gravity, the point is the center of gravity of triangle
[the idea is like this, the answer is for reference only]

In order to know that a triangle is a number, a triangle plus a triangle, a triangle minus a triangle, a triangle multiplied by a triangle, a triangle divided by a triangle, their sum is 100, what is the triangle

Let the triangle be X
2x+x^2+1=100
x^2+2x-99=0
(x-9)(x+11)=0
X = 9 or - 11