Step 1: Build a shifted alphabet strip instead of doing arithmetic letter by letter.
Write the normal alphabet, and under it write the alphabet again but moved 3 places forward (found from AIR to DLU, since A to D, I to L and R to U are each a jump of 3 letters):
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
Step 2: Read off each letter of PLANE from this strip.
Find P, L, A, N, E in the top row and read the letter directly below each one.
Under P is S.
Under L is O.
Under A is D.
Under N is Q.
Under E is H.
Step 3: Combine the results in the original order of the word.
P, L, A, N, E map to S, O, D, Q, H in that order, which spells SODQH. This lookup method gives the same word as the direct shift-by-3 calculation, which confirms the code is correct.
Final Answer:
The code for PLANE is SODQH.
\[ \boxed{\text{SODQH}} \]