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A particle is moving in the x, y plane at a speed of v = 0.80 and it is travelling an angle of 60 degrees
above the x-axis.

(a) Rotate the spatial coordinates so that v lies along the x-axis and then construct the components of the 4-velocity for the particle.

(b) Construct the remaining orthonormal basis vectors for the particle in the rotated frame, then rotate the spatial coordinates back to find the basis vectors in the original frame.

(c) Perform the same steps above but this time begin by rotating the spatial coordinates so that
v lies along the y-axis. Do you get the same result for the basis vectors after rotating back to the original frame? Should you? Draw a picture with ~v, the original (x, y) frame, and the two rotated frames to explain what is happening.