A geologist underground starts at point A whose coordinates relative to a fixed origin are (3m,−2m,1m). She then walks to point B with coordinates (−1m,5m,4m) and finally reaches point C at (4m,3m,−2m).
(i) Obtain the vector representing the change in her position from A to B.
(ii) Obtain the vector representing the change in her position from B to C.
(iii) Using your answers to (i) and (ii), find the single vector that represents the change in position from A directly to C.
(iv) Verify by explicit calculation that the result in (iii) is equal to the vector sum of the two successive changes in position.