Two vectors are given as A=2i^+3j^−6k^ and B=−4i^+3j^+2k^. Answer the following:
(i) Find the vector R=A+B.
(ii) Determine the magnitude ∣R∣.
(iii) Calculate the unit vector directed along R and express your answer with a rationalised denominator, if any.
(iv) Verify explicitly that the magnitude of the unit vector obtained in part (iii) is exactly one.