Why is normal vector n perpendicular to vector m1m2 and normal vector n perpendicular to vector m1m3, so it can be solved by vector m1m2x and vector m1m3?

Why is normal vector n perpendicular to vector m1m2 and normal vector n perpendicular to vector m1m3, so it can be solved by vector m1m2x and vector m1m3?

Because m1m2 × m1m3 is a vector product. By definition. M1m2 × m1m3 is a vector, which is perpendicular to
The plane formed by m1m2 and m1m3, m1m2 × m1m3 ⊥ m1m2, m1m2 × m1m3 ⊥ m1m3
That is, m1m2 × m1m3 can be taken as the normal vector n of the plane formed by m1m2 and m1m3

Are parallel vectors collinear? Are collinear vectors parallel?

Necessary and insufficient conditions for parallel vectors to be collinear
Necessary and sufficient condition for collinear vector to be parallel vector

How to distinguish collinear vector and parallel loudness?
If you can convince me

There is a mistake in the analysis above. The parallelism in some vectors and the parallelism in geometry are both the same and different. The vectors we learned in mathematics, including high school and undergraduate students, are all free vectors. Remember: the parallelism and collinearity of vectors are the same. Collinear vectors are parallel vectors, and parallel vectors are collinear vectors