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1- Calculate a 33 rotation matrix which rotates points about the vector A=[1,1,1] by 90 degree ?

1- Calculate a 3×3 rotation matrix which rotates points about the vector A=[1,1,1] by 90 degree ?

2- An object has a local coordinate system a=(1,0,0),b=(0,1,0),c=(0,0,1) with origin (3,2,1). Which homogeneous matrix rotates the object in to a new coordinate system u=(0,0,1),v=(0,−1,0),n=(1,0,0) with the same origin as before?

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3- show how to use a 3 dimensional matrix to rotate the unit cube about the axis defined by vector [1,1,1] ?

4-derive the transformation matrix to rotate a 3D object by angle (theta) about an arbitrary line parallel to but not coincident with z-axis
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