Consider the three vectors A=2i^−j^+2k^, B=i^+3j^−4k^ and C=−3i^+5j^+2k^.
a. (i) Evaluate the resultant vector R=A+B−C.
b. (ii) Determine the unit vector along R.
c. (iii) Given another vector S=i^+j^+k^, examine whether R and S are perpendicular. Justify your answer with appropriate calculation.