first, the dot product of (1/9)(13i- 20j- 23k) and (2i- j+ 2k) is (1/9)(26+ 20- 46)= 0 so that IS perpendicular to 2i- j+ 2k to begin with!

On the other hand, the dot product of (1/9)(13i+ 20j- 23k) and (2i- j+ 2k) is (1/9)(26- 20- 46) is NOT 0 so they are not perpendicular so D is the answer in the book it is not correct.