Two vectors are said to be equal if they have the same magnitude and direction. Equivalently they will be equal if their coordinates are equal. So two vectors a = a 1 e 1 + a 2 e 2 + a 3 e 3 and b = b 1 e 1 + b 2 e 2 + b 3 e 3 are equal if a 1 = b 1 , a 2 = b 2 , a 3 = b 3 .