If we're talking vectors in a vector space, then distributivity is taken as an axiom. We can prove it for vectors in Rn, therefore (partially) proving that our common notion of vectors actually satisfies the axioms of a vector space. Below, a and b are scalars and v and w are vectors. a(v+w) = a( (v1, ..., vn) + (w1, ..., wn) ) = a(v1+w1, ..., vnwn) = (a(v1+w1), ..., a(vn+wn)) = (av1+aw1, ... , avn+awn) = (av1, ..., avn) + (aw1, ..., awn) = av+aw (a+b)v = (a+b)(v1, ..., vn) = ((a+b)v1, ..., (a+b)vn) = (av1+bv1, ..., avn+bvn) = (av1, ..., avn) + (bv1, ..., bvn) = av+bv
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The law is used to add vectors to find the resultant of two or more vectors acting at a point.
ya they just accidentally said law of vectors instead.
If three vectors form a triangle , their vector sum is zero.
First, the word is there, not their. And, apart from you, who says there is no such law? because a*(b - c) = a*b - a*c and if that isn't the distributive property of multiplication over subtraction I don't know what is!
Distributive: a x (b + c) = (a x b) + (a x c)