Given a vector ( A ) with a magnitude of 61 and perpendicular to vector ( B ), which has a magnitude of 77, and defining ( C = A ), ( D = -B ), and ( E = -C ), determine the magnitudes of ( A ), ( B ), and ( C ).
a) ( |A| = 61 ), ( |B| = 77 ), ( |C| = 61 )
b) ( |A| = 61 ), ( |B| = 77 ), ( |C| = 77 )
c) ( |A| = 77 ), ( |B| = 61 ), ( |C| = 61 )
d) ( |A| = 77 ), ( |B| = 61 ), ( |C| = 77 )