Foundations of Virtual Reality Nptel Week 4 Answers
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Foundations of Virtual Reality Nptel Week 4 Answers (July-Dec 2025)
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Question 1. Which one of the following quaternions is a rotation by -60 degrees around vector v = (-1, -1, 0)?
Note that:
cos(30°) = √3/2, sin(30°) = 1/2
cos(60°) = 1/2, sin(60°) = √3/2
a) q1 = (√3/2, 1/2√2, 1/2√2, 0)
b) q3 = (1/2, √3/2, √3/2, 0)
c) q2 = (√3/2, 1/2, 0, 0)
d) q4 = (√3/3, √3/3, √3/3, 0)
e) None of the above
Question 2. Which one is Not a Unit Quaternion?
a) (√3/2, 1/2√2, 1/2√2, 0)
b) (1/2, √3/2, 0, 0)
c) (√3/2, 1/2, 1/2, 0)
d) (√3/3, √3/3, 0, √3/3)
e) More than one above
Question 3. Which one is the inverse of the quaternion q = (-1, 0, 0, 0)?
a) (-1, 0, 0, 0)
b) (0, -1, 0, 0)
c) (0, 0, -1, 0)
d) (0, 0, 0, -1)
e) None of the above
These are Foundations of Virtual Reality Nptel Week 4 Answers
Question 4. What is the best description of the following matrix?
⎡ -1 0 0 0 ⎤
⎢ 0 1 0 0 ⎥
⎢ 0 0 -1 0 ⎥
⎣ -1 1 -1 1 ⎦
a) Translate by (-1, 1, -1) only
b) Translate by (-1, 1, -1) and then convert from right-handed coordinate frame to left-handed
c) First translate by (-1, 1, -1) and then rotate by a yaw of 180° (in global frame)
d) First rotate by a yaw of 180°, and then translate by (-1, 1, -1) (in global frame)
e) None of the above
Question 5. Which one is an equivalent to the following matrix?
⎡ -1 0 0 0 ⎤
⎢ 0 1 0 0 ⎥
⎢ 0 0 -1 0 ⎥
⎣ -1 1 -1 1 ⎦
a) [Matrix Option 1]
b) [Matrix Option 2]
c) [Matrix Option 3]
d) [Matrix Option 4]
e) None of the listed
Question 6. Which one is the inverse of the following matrix?
⎡ -1 0 0 0 ⎤
⎢ 0 1 0 0 ⎥
⎢ 0 0 -1 0 ⎥
⎣ -1 1 -1 1 ⎦
a) [Matrix Option 1]
b) [Matrix Option 2]
c) [Matrix Option 3]
d) [Matrix Option 4]
e) None of the listed
Question 7. Consider an object (letter R) originally placed flat in the XZ plane with its vertical portion aligned with the X axis. Which one is the chain of quaternions that represent the rotation of the object to the XY plane, aligned with (1, 1, 0)?
a) (cos 45°, 0, 0, sin 45°)(cos 90°, sin 90°, 0, 0)
b) (cos 45°, sin 45°, 0, 0)(cos, 0, 0, sin)
c) (cos 90°, 0, 0, sin 90°)(cos 45°, sin 45°, 0, 0)
d) (cos 45°, sin 45°, 0, 0)(cos 90°, 0, 0, sin 90°)
e) None of the above
These are Foundations of Virtual Reality Nptel Week 4 Answers
Question 8. Which image properly represents Steve’s new configuration?
Steve performs:
- rotate by yaw -90° (around y)
- translate by (0,0,5)
a) Option 1
b) Option 2
c) Option 3
d) Option 4
e) None of the above
Question 9. Which quaternion properly represents Steve’s new orientation?
a) (√2, 0, √2, 0)
b) (√2, 0, -√2, 0)
c) (√2, -√2, -√2, 0)
d) (√2, √2, √2, 0)
e) None of the above
Question 10. Which matrix properly represents Steve’s new configuration?
Steve performs:
- rotate by yaw -90° (around y)
- translate by (0,0,5)
a) [Matrix Option 1]
b) [Matrix Option 2]
c) [Matrix Option 3]
d) [Matrix Option 4]
e) None of the above
These are Foundations of Virtual Reality Nptel Week 4 Answers