(a) State the commutative and associative properties of vector addition.
(b) Do the same properties hold for vector subtraction? Give a clear conceptual explanation based on the idea of “adding the negative of a vector”.
(c) Construct an explicit counter-example using three non-zero vectors of your choice that shows vector subtraction fails to be both commutative and associative. Show all working and justify each conclusion.
b. (b) Explain whether these properties hold for vector subtraction, giving conceptual reasons.
c. (c) Provide a counter-example with three explicit vectors to demonstrate that subtraction is neither commutative nor associative.