# Computer Graphics Questions & Answers – 3D Rotation – 2

This set of Computer Graphics Multiple Choice Questions & Answers (MCQs) focuses on “3D Rotation – 2”.

1. Which of the following equation is correct for the new Z co-ordinate if an object undergoes 3D rotation around x axis?
a) Znew = Yold x sinθ – Zold x cosθ
b) Znew = Yold x sinθ + Zold x cosθ
c) Znew = Yold x cosθ – Zold x sinθ
d) Znew = Yold x cosθ + Zold x sinθ

Explanation: The correct equation for the new Z co-ordinate if an object undergoes 3D rotation around x axis is – Znew = Yold x sinθ + Zold x cosθ.
When the matrix form for 3D rotation around x axis is expanded then we get the following equations – Xnew = Xold; Ynew = Yold x cosθ – Zold x sinθ; Znew = Yold x sinθ + Zold x cosθ.

2. Which of the following equation is correct for the new X co-ordinate if an object undergoes 3D rotation around y axis?
a) Xnew = Zold x cosθ – Xold x sinθ
b) Xnew = Zold x cosθ + Xold x sinθ
c) Xnew = Zold x sinθ – Xold x cosθ
d) Xnew = Zold x sinθ + Xold x cosθ

Explanation: The correct equation for the new X co-ordinate if an object undergoes 3D rotation around y axis is – Xnew = Zold x sinθ + Xold x cosθ
When the matrix form for 3D rotation around y axis is expanded then we get the following equations – Xnew = Zold x sinθ + Xold x cosθ; Ynew = Yold; Znew = Yold x cosθ – Xold x sinθ

3. Which of the following equation is correct for the new X co-ordinate if an object undergoes 3D rotation around z axis?
a) Xnew = Xold x cosθ – Yold x sinθ
b) Xnew = Xold x cosθ + Yold x sinθ
c) Xnew = Xold x sinθ – Yold x cosθ
d) Xnew = Xold x sinθ + Yold x cosθ

Explanation: The correct equation for the new X co-ordinate if an object undergoes 3D rotation around z axis is – Xnew = Xold x cosθ – Yold x sinθ
When the matrix form for 3D rotation around z axis is expanded then we get the following equations – Xnew = Xold x cosθ – Yold x sinθ; Ynew = Xold x sinθ + Yold x cosθ; Znew = Zold

4. Which of the following equation is correct for the new Y co-ordinate if an object undergoes 3D rotation around z axis?
a) Ynew = Xold x sinθ – Yold x cosθ
b) Ynew = Xold x sinθ + Yold x cosθ
c) Ynew = Xold x cosθ – Yold x sinθ
d) Ynew = Xold x cosθ + Yold x sinθ

Explanation: The correct equation for the new Y co-ordinate if an object undergoes 3D rotation around z axis is – Ynew = Xold x sinθ + Yold x cosθ
When the matrix form for 3D rotation around z axis is expanded then we get the following equations – Xnew = Xold x cosθ – Yold x sinθ; Ynew = Xold x sinθ + Yold x cosθ; Znew = Zold.

5. What will be the final coordinates after rotation of the point P(5, 5, 5) at 90° about Z-axis?
a) (5, -5, -5)
b) (-5, -5, -5)
c) (-5, 5, 5)
d) (5, -5, 5)

Explanation: According to the equations –
Xnew = Xold x cosθ – Yold x sinθ = 5 x 0 – 5 x 1 = -5
Ynew = Xold x sinθ + Yold x cosθ = 5 x 1 + 5 x 0 = 5
Znew = Zold = 5
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6. What will be the final coordinates after rotation of the point P(2, 3, 7) at 90° about X-axis?
a) (2, -7, -3)
b) (-2, -7, -3)
c) (-2, 7, 3)
d) (2, -7, 3)

Explanation: According to the equations –
Xnew = Xold = 2
Ynew = Yold x cosθ – Zold x sinθ = 3 x 0 -7 x 1 = -7
Znew = Yold x sinθ + Zold x cosθ = 3 x 1 + 7 x 0 = 3

Sanfoundry Global Education & Learning Series – Computer Graphics.