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yanyin
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Hi, if i want to find a 3x3 matrix R which represents a rotation of Pi/6 around the axis of rotation v(vector)={1, 2, 3}. how can i find it?
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Thanks. it's a vector from origin to (1, 2, 3). which direction? i am not sure yet. let say clockwise.Originally posted by Janitor
Are you saying that your axis is along a vector that starts at the origin of the coordinate system and has its tip at the point (x,y,z)=(1,2,3)? And is your rotation direction clockwise or counterclockwise as viewed from the perspective of (0,0,0)?
To find a 3x3 rotation matrix, you can use the basic formula for a rotation matrix in 3D space:
R = [cosθ -sinθ 0
sinθ cosθ 0
0 0 1]
where θ is the angle of rotation. This formula can be modified for different axes of rotation or to rotate around a specific point.
A 3x3 rotation matrix is used to represent and perform rotations in 3D space. It is commonly used in computer graphics, robotics, and other fields where 3D rotations need to be calculated and applied.
To multiply two 3x3 rotation matrices, you can use the matrix multiplication formula:
[R1] x [R2] = [R]
where R1 and R2 are the two rotation matrices and R is the resulting matrix. Note that the order of multiplication matters, as matrix multiplication is not commutative.
No, a 3x3 rotation matrix is only used for rotation in 3D space. Scaling and translation are represented by different types of matrices.
A 3x3 rotation matrix has 3 degrees of freedom, as it can represent rotations around the x, y, and z axes. This means that it can represent any rotation in 3D space using just 3 parameters.