Non commutative and distributive law of vector product

a.a=|a|^(2) and commutative and distributive law of dot product

Commutative law

Wien's distribution law fails at

Distributive law is obeyed by

In the following questions a statement of assertion (A) is followed by a statement of reason ( R). A : The addition of two vectors vecP and vecQ is commutative R: By triangle law of vector addition we can prove vecP+vecQ=vecQ+vecP .

Are the commutative law and associtive law applicable to vectors subtraction.

Theorem 5 (distributive Laws)

The law a+b=b+a is called (a) closure law (b) associative law (c) commutative law (d) distributive law

Subtraction of integers is commutative but not associative commutative and associative associative but not commutative (d) neither commutative nor associative

Property 8: Distributivity of vector product over vector addition