QUESION5
Local Rotation
Choose one $\cdot 5$ points
Write the local rotation matrix of 90 about the local Zaxis, $^{B_{Z}} (90)$
$(\begin{array}{ccc} 0 & 1 & 0 \\ - 1 & 0 & 0 \\ 0 & 0 & 1 \end{array})$
$(\begin{array}{ccc} 0 & - 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array})$
$(\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array})$

Answer

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Final Answer: The local rotation matrix of 90 degrees about the local Z-axis is $[\begin{matrix} 0 & - 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]$

Steps

Step 1 ：The problem is asking for the local rotation matrix of 90 degrees about the local Z-axis.

Step 2 ：The rotation matrix for a 90 degree rotation about the Z-axis is given by: $[\begin{matrix} c o s (90) & - s i n (90) & 0 \\ s i n (90) & c o s (90) & 0 \\ 0 & 0 & 1 \end{matrix}]$

Step 3 ：In this case, cos(90) = 0 and sin(90) = 1.

Step 4 ：So the rotation matrix becomes: $[\begin{matrix} 0 & - 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]$

Step 5 ：Final Answer: The local rotation matrix of 90 degrees about the local Z-axis is $[\begin{matrix} 0 & - 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]$

QUESION5Local RotationChoose one ⋅5 pointsWrite the local rotation matrix of 90 about the local Zaxis, BZ(90)(010−100001)(0−10100001)(010100001)

Answer

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