When the force is perpendicular to the coordinate axis, does the projection of the force on that axis remain unchanged or equal to zero?

When the force is perpendicular to the coordinate axis, does the projection of the force on that axis remain unchanged or equal to zero?

Because the formula of vector projection is: the modulus of vector a times cos
So the answer should be 0

Projection component
What is the difference between the projection of force on the coordinate axis and the component of force on the coordinate axis?
It seems that the difference is great when the coordinate axes are not perpendicular to each other. This is a problem I encountered in theoretical mechanics

Projection is the vertical projection of the action line of the force on the coordinate axis, which emphasizes the perpendicularity of the auxiliary line. The component force is decomposed according to the angle of the coordinate axis, just like the decomposition of the parallelogram, and the auxiliary line is not necessarily perpendicular to the coordinate axis. I don't know if I have made it clear
Since you all know that when the coordinate axes are not perpendicular to each other, it's very different. Why not draw a picture?

What's the difference between projection and component force? What's the solution of the term "rigid body" in the translation theorem of force

Projection is a concept of vector in mathematics. It is a vector multiplied by cos θ. θ is the angle between this vector and another vector. The result is the projection of this vector on another vector. Component force is a physical concept, and component force is an application of projection. Rigid body is an ideal object whose shape and size will not change after being acted by force

Let the projection points of M (1,1,1) on the coordinate axis be a, B and C respectively, and solve the plane equations of a, B and C

Let the projection points of M (1,1,1) on the coordinate axis be a, B and C respectively,
The coordinates of the three points are: (1,0,0) (0,1,0) (0,0,1)
therefore
Through the plane equation of a, B, C, according to the intercept formula can be obtained
x/1+y/1+z/1=1
Namely
x+y+z-1=0