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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

Q: How to proof the distributive law in vectors?

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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!

Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.

Related questions

two numbers multiply one another

law of vectors also include the parallellogram law .

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.

according to commutative property both the distributive laws are equal why to use two distributive laws

If three vectors form a triangle , their vector sum is zero.

there are 3 laws of arithmetic. These are Associative law, Distributive Law and Cummutative law.

You will need to use the distributive law to solve discrete series by grouping. The distributive law is a(b + c) = ab + ac. You will be removing the common factors as you go.

For any two numbers a and b: a + b = b + a and a * b = b * a Substitute any two numbers you like and perform the indicated operations. There is no distributive law of subtraction or division.

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!

A law which states that if a body is acted upon by two vectors represented by two sides of a triangle taken in order, the resultant vector is represented by the third side of the triangle.

Yes.