Let's analyze the image of the cube $ABCD.EFGH$ and solve the questions step by step:

a. Garis yang berpotongan dengan garis CG

• Garis $CG$ is a diagonal of the face $BCGF$.
• Lines that intersect $CG$ include lines on the face $BCGF$ or extending diagonally.
• Answer: The line $EG$ (diagonal of face $EGHD$) intersects $CG$ at point $G$.

b. Titik yang terletak pada bidang ADGF

• The plane $ADGF$ consists of points $A, D, G, F$.
• Any point on this plane belongs to the edges of these vertices.
• Answer: Possible points include $A, D, G, F$ since they form the plane $ADGF$.

c. Titik yang terletak di luar bidang BCHE

• The plane $BCHE$ consists of points $B, C, H, E$.
• Any point outside this plane will be vertices not on this face.
• Answer: Possible points outside $BCHE$ are $A, D, F, G$.

d. Garis yang memotong bidang BCGF

• The plane $BCGF$ consists of lines and edges connecting the points $B, C, G, F$.
• Any line cutting through this plane but not lying on it would pass through.
• Answer: The line $AE$ intersects this plane at some internal point but does not lie on it.

e. Panjang proyeksi $AF$ pada bidang ACGE

• To calculate the projection of line $AF$ onto plane $ACGE$, note that $AF$ is a diagonal and lies partly along $ACGE$, but its projection depends on the angle between the line and the plane.
• Answer: The projection is calculated using vector mathematics, but geometrically, the projection will equal the perpendicular distance from $F$ to the plane, which can be determined from cube dimensions.

Would you like further elaboration on any of these answers or details on projection calculations?

Follow-up questions:

1. How do we find the equation of the plane $ACGE$?
2. What is the general formula for finding the projection of a line onto a plane?
3. How can we calculate the distance between a point and a plane in 3D geometry?
4. Can we use vectors to solve more general problems in cubic structures?
5. What would be the length of the diagonal $AG$ in the cube?

Tip: When dealing with projections, understanding vector components and dot products can help simplify calculations!