The head-to-tail method gives the same resultant regardless of the order the vectors are drawn because vector addition is:

1. The resultant runs from the tail of the first vector to the head of the last. 2. Drawing a line from the tail of the east-pointing vector to the head of the north-pointing vector forms the resultant. 3. Walking east then north arrives at the same corner as walking north then east. 4. So the order of drawing does not change where the resultant ends up. 5. The method also extends to any number of vectors, not just two. _Source: OpenStax College Physics for AP(R) Courses 2e (CC BY 4.0), Ch 3 'Two-Dimensional Kinematics', sections 3.1-3.4_