Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
-Rotation about the y-axis through an angle of 60° 73)
A)
$$\left[ \begin{array} { c c c c }
0.5 & 0 & \sqrt { 3 } / 2 & 0 \
0 & 1 & 0 & 0 \
- \sqrt { 3 } / 2 & 0 & 0.5 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$
B)
$$\left[ \begin{array} { c c c c }
\sqrt { 3 } / 2 & 0 & 0.5 & 0 \
0 & 1 & 0 & 0 \
- 0.5 & 0 & \sqrt { 3 } / 2 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c c c }
0.5 & \sqrt { 3 } / 2 & 0 & 0 \
- \sqrt { 3 } / 2 & 0.5 & 0 & 0 \
0 & 0 & 1 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$
D)
$$\left[ \begin{array} { c c c c }
1 & 0 & 0 & 0 \
0 & 0.5 & \sqrt { 3 } / 2 & 0 \
0 & - \sqrt { 3 } / 2 & 0.5 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$

Question

Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
-Rotation about the y-axis through an angle of 60° 73) 
A)
$$\left[ \begin{array} { c c c c } 
0.5 & 0 & \sqrt { 3 } / 2 & 0 \
0 & 1 & 0 & 0 \
- \sqrt { 3 } / 2 & 0 & 0.5 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$
B)
$$\left[ \begin{array} { c c c c } 
\sqrt { 3 } / 2 & 0 & 0.5 & 0 \
0 & 1 & 0 & 0 \
- 0.5 & 0 & \sqrt { 3 } / 2 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$
C)
$$\left[ \begin{array} { c c c c } 
0.5 & \sqrt { 3 } / 2 & 0 & 0 \
- \sqrt { 3 } / 2 & 0.5 & 0 & 0 \
0 & 0 & 1 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$
D)
$$\left[ \begin{array} { c c c c } 
1 & 0 & 0 & 0 \
0 & 0.5 & \sqrt { 3 } / 2 & 0 \
0 & - \sqrt { 3 } / 2 & 0.5 & 0 \
0 & 0 & 0 & 1
\end{array} \right]$$

Quizplus · Accepted Answer

The correct answer is A because it is the only matrix that produces a rotation about the y-axis through an angle of 60°.

Find the 4 × 4 Matrix That Produces the Described