Solve the each part of given problem:

Problem: A particle moves with constant velocity. Its position vectors at two different times are shown in the picture. (Position r1 occurs earlier than r2). Let |r1|=|r2|, and the angle each vector makes (theta) measured from the + axis be 45 degrees, such that r1 is orthogonal to r2.

Part A: What is the direction of the velocity of the particle?

Part B: Sketch the resultant velocity vector on the above plot. Make sure the direction is consistent with your answer to part (a)?

Part C: Calculate the projection of r1 onto r2. How does it compare to the projection of r2 onto r1. Justify your answer.

Please show your results in detailed calculations.