A particle is traveling along an arc of 6.5 inch radius. The arc center is at the origin of a coordinate system. When the particle is at position A, its position vector makes a 45-deg angle with the X axis. At position B, its vector makes a 75-deg angle with the X axis. Draw this system to some convenient scale and: a. Write an expression for the particle's position vector in position A using complex number notation, in both polar and Cartesian forms.
b. Write an expression for the particle's position vector in position B using complex number notation, in both polar and Cartesian forms.
c. Write a vector equation for the position difference between points B and A. Substitute the complex number notation for the vectors in this equation and solve for the position difference numerically.
d. Check the result of part c with a graphical method.