Any vector in an arbitrary direction can always be replaced by two (or three):
\[{\text{A}}{\text{. }}\] Parallel vectors which have the original vector as their resultant
${\text{B}}{\text{.}}$ Mutually perpendicular vectors which have the original vector as their resultant
${\text{C}}{\text{.}}$ Arbitrary vectors which have the original vector as their resultant
${\text{D}}{\text{.}}$ It is not possible to resolve a vector

- Hint – To solve this type of question first we have a good understanding of resolving a vector and knowledge of properties of vectors and knowledge of types of vectors.

Complete step-by-step solution -

We have in option A Parallel vectors which have the original vector as their resultant so this option is correct because we have to satisfy the condition ‘ original vector as their resultant ‘ and in this option this condition is satisfied so option A is the correct option.
Now we have in option B ‘ mutually perpendicular vectors which have the original vector as their resultant’ here also our condition ‘ original vector as their resultant ‘ is satisfied so option B is the correct option.
Now we have in option C ‘ Arbitrary vectors which have the original vector as their resultant ‘ here also our condition ‘ original vector as their resultant ‘ is satisfied so option C is the correct option.
Now in option D ‘ It is not possible to resolve a vector ‘ is absolutely wrong because we have already resolved all three options.

Note: Whenever we get this type of question the key concept of solving is we have to focus on our criteria which is satisfied or not here that criteria was resultant vector should be the original vector and just we have to check this for the correct answer.