Is the use of word-'both' with plural nouns correct in the sentence below

Sentence => ‘Two or more vectors are said to be equal vectors when both of their magnitudes and directions are same.’

In the above sentence I have used the word-‘both’ with the words- ‘magnitudes’ and ‘directions’ which are in plural form because the sentence is referring to two vectors which each have some magnitude and a direction.

Please also tell if there is an other error or if the sentence can be written in another way.