Question

Perspective view of an object is shown below. The object is rotated 90 degrees anticlockwise about z-axis (when viewed from a point on the positive z-axis towards the origin) and then rotated 180 degrees about x-axis (when viewed from a point on the positive x-axis towards the origin). Which one of the following perspective view options will be the result of the rotations? 

• A. A
• B. B
• C. C
• D. D

Hint:

For sequential 3D rotations, do not try to visualize the entire process at once. Perform one rotation at a time. Tracking a single, prominent feature or corner of the object through the transformations makes the problem much easier to solve.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept: 
This problem involves performing a sequence of 3D rotations on an object and identifying the final orientation. It is crucial to perform the rotations in the correct order and around the correct axes. 
Step 2: Detailed Explanation: 
Let's track the orientation of a distinct part of the object, for example, the highest T-junction. 
Initial Position: 
A vertical segment points in the +z direction (up). 
From the top of this segment, another segment branches out in the +y direction (away from the viewer, into the page). 
Rotation 1: 90 degrees anticlockwise about z-axis. 
This rotation occurs in the x-y plane. 
A point at (x, y) moves to (-y, x). 
The vertical segment along the z-axis does not change its direction. It still points up (+z). 
The segment that was pointing in the +y direction will now point in the -x direction (to the left). 
After Rotation 1: The T-junction has a vertical segment pointing up (+z) and a horizontal segment pointing left (-x). 
Rotation 2: 180 degrees about x-axis. 
This rotation flips the y and z coordinates. A point at (x, y, z) moves to (x, -y, -z). 
The vertical segment that was pointing up (+z) will now flip and point down (-z). 
The horizontal segment that was pointing in the -x direction lies on the axis of rotation (or is parallel to it). A rotation about the x-axis does not change the x-coordinate. So, it will still point in the -x direction. 
After Rotation 2 (Final Position): The T-junction has a vertical segment pointing down (-z) and a horizontal segment pointing left (-x). 
Step 3: Comparing with Options: 
Let's find the option that matches this final orientation. 
(A): This view shows the object with the main vertical stem pointing downwards. The T-junction at its end has a segment pointing to the left (-x direction). This perfectly matches our derived final position. 
(B): The stem points down, but the horizontal segment points away (+y direction). Incorrect. 
(C): The stem points up. Incorrect. 
(D): The stem points down, but the horizontal segment points to the right (+x direction). Incorrect. 
Step 4: Final Answer: 
The final orientation of the object after both rotations is correctly shown in option (A).