Answer
c. \( (2,1,1) \): A ray of light originating at \( (2,1,1) \) would strike the surface of the patch from inside the object.
Work Step by Step
To determine whether a ray of light originating at a given point would strike the surface of the patch from outside or inside the object, we need to consider the orientation of the vertices of the patch.
Given the vertices \( (1,0,0), (1,1,1), \) and \( (1,0,2) \), listed in a counter-clockwise order as seen from outside the object, we can observe that the normal vector to the patch points outward from the object.
a. \( (0,0,0) \): This point is outside the object, as it lies on the negative side of the x-axis. A ray of light originating from this point would strike the surface of the patch from outside.
b. \( (2,0,0) \): This point is also outside the object, as it lies on the positive side of the x-axis. A ray of light originating from this point would strike the surface of the patch from outside.
c. \( (2,1,1) \): This point is inside the object, as it lies between the points \( (1,0,0) \) and \( (1,0,2) \). A ray of light originating from this point would strike the surface of the patch from inside.
d. \( (3,2,1) \): This point is outside the object, as it lies on the positive side of the x-axis. A ray of light originating from this point would strike the surface of the patch from outside.
Correct answer:
c. \( (2,1,1) \): A ray of light originating at \( (2,1,1) \) would strike the surface of the patch from inside the object.
