Question

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Explanation:

Step1: Verify parallel line (Q1)

In a cube, $\overrightarrow{AJ}$ is an edge; $\overrightarrow{GF}$ is parallel (same direction, no intersection).

Step2: Verify perpendicular line (Q2)

$\overrightarrow{BC}$ is a horizontal edge; $\overrightarrow{AB}$ meets it at 90°, so perpendicular.

Step3: Verify parallel plane (Q3)

Plane AFH faces plane DGE (no intersecting lines, cube opposite faces).

Step4: Verify skew line (Q4)

$\overrightarrow{GF}$ and $\overrightarrow{AC}$ are non-coplanar, no intersection, so skew.

Step5: Identify line type (Q5)

Definition: Non-coplanar, non-intersecting lines are skew.

Step6: Solve for x (Q6)

Sum of angles = 180°:
$$4x + x + 90 = 180$$
Simplify:
$$5x = 90$$
$$x = \frac{90}{5} = 18$$

Answer:

1. $\overrightarrow{GF}$
2. $\overrightarrow{AB}$ (or any edge perpendicular to $\overrightarrow{BC}$, e.g., $\overrightarrow{BF}$)
3. Plane DGE
4. $\overrightarrow{AC}$
5. [D] skew
6. $x=18$