A geologist underground starts at point A whose coordinates relative to a fixed origin are

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A geologist underground starts at point A whose coordinates relative to a fixed origin are (3 m,  −2 m,  1 m)(3\,\text{m},\;-2\,\text{m},\;1\,\text{m}). She then walks to point B with coordinates (−1 m,  5 m,  4 m)(-1\,\text{m},\;5\,\text{m},\;4\,\text{m}) and finally reaches point C at (4 m,  3 m,  −2 m)(4\,\text{m},\;3\,\text{m},\;-2\,\text{m}). (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.

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