Two displacement vectors are added tip-to-tail in either order
MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors
Problem
Two displacement vectors are added tip-to-tail in either order, yet the same resultant vector is obtained. Which of the following best explains this outcome?
(a) Vector addition is associative, so rearranging the vectors does not affect the resultant.
(b) The commutative property works only when the two vectors are perpendicular, and that is why the order can be swapped here.
(c) The resultant depends only on the magnitudes of the vectors, so reversing the order does not change it.
(d) Vector addition is commutative because each vector contributes independently to the perpendicular components of the resultant.