prove that if a is not equal to zero and if a �* b = a * c and a ^ b = a ^ c then b = c [Hint: calculate a �* (b-c) and a ^ (b-c) vectors mechanics
a*b = a*c
a*b - a*c = 0
a*(b-c) = 0
if a≠0, b-c = 0, since the product is zero.
b-c = 0
b = c
a^b = a^c
a^b / a^c = 1
a^(b-c) = a^0
b-c = 0
b = c