Question

Two views of a 3D object are shown on the left. Which of the option(s) is/are the same object?

• A. Fig A
• B. Fig B
• C. Fig C
• D. Fig D

Hint:

Pick an asymmetrical feature as your anchor (like the single arm going upward). Note the direction it points relative to the other arms. If an option shows that anchor pointing to the wrong side of the trunk, it is a mirror reflection.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are provided with two reference perspective drawings of a complex 3D pipe/wireframe structure composed of orthogonal square-section segments. We must rotate this mental model in 3D space to identify which of the four options (A, B, C, D) depict the exact same geometry.

Step 2: Key Formula or Approach:
To ensure an option is an authentic rotation rather than a distinct shape or mirror image:

• Verify branch count and relative branch vectors stemming from the central trunk.

• Trace the directional step sequence along each arm to verify segment length ratios.

• Check the structural chirality (handedness) of the bends. A mirror reflection flips the cross-product signs and cannot be aligned via rotation.


Step 3: Detailed Explanation:

• Analyzing the reference views reveals a central trunk with three branching arms:
- One arm travels upward, executing two 90-degree turns to form an elevated U-shaped step.
- The other two arms travel downward, executing symmetric steps that project below the central junction.

• Let us evaluate the options:
-

Option A: Shows the elevated upper arm bending in the reverse direction relative to the lower arms. Sinking this model into coordinate space confirms it has opposite chirality. It is a mirrored enantiomer, not a rotated view. Therefore, Option A is incorrect.
-

Option B: Rotating the reference object around the vertical axis by roughly 120 degrees and adjusting the pitch brings it into this exact orientation. Every segment length and bend direction aligns perfectly. Therefore, Option B is correct.
-

Option C: Features noticeable distortions in the proportional lengths of the terminal segments compared to the original drawing. Therefore, Option C is incorrect.
-

Option D: Represents another valid spatial rotation of the identical wireframe, viewed from a slightly different elevation angle. Therefore, Option D is correct.


Step 4: Final Answer:
Options (B) and (D) show the correct rotated views of the object.