A hiker follows three successive displacement vectors: p=4km due east, q=3km due north and r=2km due west.
(i) Express p,q,r in unit-vector notation taking east as i^ and north as j^.
(ii) Compute the resultant displacement when the vectors are added in the order (p+q)+r.
(iii) Compute the resultant displacement when the vectors are added in the order p+(q+r).
(iv) Explain why the two results must be identical, referring to the relevant property of vector addition.
(v) If the hiker instead performs the vectors in the order q+p+r, will the final position change? Justify your answer.
a. (i) Write p,q,r in unit-vector form.
b. (ii) Compute (p+q)+r.
c. (iii) Compute p+(q+r).
d. (iv) Explain the equality of the two results obtained in (ii) and (iii).
e. (v) Analyse whether adding in the order q+p+r affects the resultant and state the underlying principle.