On the vector coordinate calculation of unity3d, quaternion and vector multiplication? Quaternion.Euler (0,90,0)*Vector3(0.0,0.0,-10) Why can we get a new vector centered on the origin, 10 units from the origin, and rotated 90 degrees around the Y axis?

Quaternion.Euler (x, y, z) returns a quaternion that rotates x degrees around the X axis, y degrees around the Y axis, and Z degrees around the Z axis Quaternion.Euler (0,90,0) returns a rotation operation that rotates 90 degrees around the Y axis
Quaternion's right multiply operation (*) on vector3 returns a vector after rotating it
therefore Quaternion.Euler (0,90,0) * vector3 (0.0,0.0, - 10) represents the result of rotating vector vector3 (0.0,0.0, - 10) 90 degrees around the y-axis, which is equal to vector3 (- 10,0,0)

What is the result of multiplication of matrix and vector?
If a is an n-dimensional column vector and a is a matrix of order n, then a · A is a matrix or a vector. Why?

Vectors are special matrices
A matrix with only one row or column is called a vector
If a is an n-dimensional column vector and a is a matrix of order n, then a is a matrix with only one column, which is called a vector
If we call it a vector, our first impression is that it has only one row or one column
If you call it a matrix, you have to say that it has only one column

What is the trajectory equation of the center of a moving circle tangent to the X axis and circumscribed to the circle x ^ 2 + y ^ 2 = 1?

Let P (x1, Y1) be the center of the circle
Because the radii of the circles are equal
|y1|=√（（x1）^2+（y1）^2）-1
y1^2=x1^2+y1^2+1-2√（（x1）^2+（y1）^2）
2√（（x1）^2+（y1）^2）=x1^2+1
Square, then root
x1-2y1-1=0
x-2y-1=0

On the vector coordinate calculation of unity3d, quaternion and vector multiplication? Quaternion.Euler (0,90,0)*Vector3(0.0,0.0,-10) Why can we get a new vector centered on the origin, 10 units from the origin, and rotated 90 degrees around the Y axis?