Does any one know how to proof the distributive law in vector product. please hel me?

hay guys i have a big problem with proofing the distributive law in vector product or vector product proof in distributive law.


i dont know how to proof it in a easy way , the main formula is:





vector a X( vector b+ vector c )= vector a X vector b+ vector a X vector c. i have to proof the formula.





big X is not the sign of multiplaction, its just cros in vectors. i hope you guys know what i mean.

Does any one know how to proof the distributive law in vector product. please hel me?
Let vector a be %26lt;a1, a2, ...., an%26gt;.


Let vector b be %26lt;b1, b2, ...., bn%26gt;.


Let vector c be %26lt;c1, c2, ...., cn%26gt;.





vector a X( vector b+ vector c )


%26lt;a1, a2, ...., an%26gt; X (%26lt;b1, b2, ...., bn%26gt; + %26lt;c1, c2, ...., cn%26gt;)


%26lt;a1, a2, ...., an%26gt; X (%26lt;b1+c1, b2 + c2, ...., bn + cn%26gt;)


%26lt;a1(b1+c1), a2(b2 + c2), ...., an(bn + cn)%26gt;


%26lt;a1b1+a1c1, a2b2 + a2c2, ...., anbn + ancn%26gt;


%26lt;a1b1, a2b2, anbn%26gt;+ %26lt;a1c1, a2c2, ...., ancn%26gt;


%26lt;a1, a2, ...., an%26gt; X %26lt;b1, b2, ...., bn%26gt; + %26lt;a1, a2, ...., an%26gt; X %26lt;c1, c2, ...., cn%26gt;


vector a X vector b+ vector a X vector c





QED

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