Let us say you have a vector, v, represented by 1. Active and Passive Rotations the point (3,4) on a 2-D cartesian coordinate system. Now let us rotate the coordinate system such that the same vector lies on the x-axis. What is the representation of the same vector in the new coordinate system? By what angle did we rotate the coordinate system? Now do the same for a general coordinate system rotation (Assume you rotate the coordinate system by some theta 9 and find the coordinates of the vector in the new coordinates as a function of theta). Now, what if instead the coordinate system is kept fixed and the vector is rotated by an angle 0? What are the coordinates of the new vector? +* X

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