Question

State the laws of addition of parallelogram numerically with theory.

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Answer 1

♡hello dearie♡

the statement of the paddle gram law of vector addition speak something like this. if two vectors acting at a point are represented. in magnitude and direction by the two others and sides of a parallelogram drawn. ... in magnitude direction by the two adjacent sides of a parallelogram.

Numerically solve:-

Let a,ba,b be two vectors & let these constitute the sides of a parallelogram such that they are co-initial from one of the vertices of a parallelogram. So, considering assumption that the law be true(this is what we'll judge now whether by taking the assumption for the validity of the law, we can prove something which is earlier ascertained by elementary geometry), the two diagonals are a+b,b−aa+b,b−a. Sum of the squares of the diagonals is |a+b|2+|b−a|2|a+b|2+|b−a|2. Now, from Euclidean Geometry, we get from Parallelogram law which states that,

The sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals.11

So, the sum of the squares of the diagonals i.e. |a+b|2+|b−a|2|a+b|2+|b−a|2must be equal to the sum of the squares of the sides 2(|a|2+|b|2)2(|a|2+|b|2).

This can be proved by inner product or for this case dot product.

|a+b|2+|b−a|2=(a+b)⋅(a+b)+(b−a)⋅(b−a)⟹|a+b|2+|b−a|2=2a⋅a+2b⋅b=2(|a|2+|b|2)|a+b|2+|b−a|2=(a+b)⋅(a+b)+(b−a)⋅(b−a)⟹|a+b|2+|b−a|2=2a⋅a+2b⋅b=2(|a|2+|b|2)

which makes our assumption that the law is true absolutely true.


Attachment of pitcure....

hope it helps uu...!!!❤

#Dramaqueen⭐

Answer 2

heya...

✔here is ua answer:

✔The statement of the parallelogram about the law of vector says that if two vectors acting at a point are represented. in magnitude and direction by the two others and sides of a parallelogram drawn. ... in magnitude direction by the two adjacent sides of a parallelogram.

Numerically solve:-

Let a,ba,b be two vectors & let these constitute the sides of a parallelogram such that they are co-initial from one of the vertices of a parallelogram. So, considering assumption that the law be true(this is what we'll judge now whether by taking the assumption for the validity of the law, we can prove something which is earlier ascertained by elementary geometry), the two diagonals are a+b,b−aa+b,b−a. Sum of the squares of the diagonals is |a+b|2+|b−a|2|a+b|2+|b−a|2. Now, from Euclidean Geometry, we get from Parallelogram law which states that,

The sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals.11

So, the sum of the squares of the diagonals i.e. |a+b|2+|b−a|2|a+b|2+|b−a|2must be equal to the sum of the squares of the sides 2(|a|2+|b|2)2(|a|2+|b|2).

This can be proved by inner product or for this case dot product.

|a+b|2+|b−a|2=(a+b)⋅(a+b)+(b−a)⋅(b−a)⟹|a+b|2+|b−a|2=2a⋅a+2b⋅b=2(|a|2+|b|2)|a+b|2+|b−a|2=(a+b)⋅(a+b)+(b−a)⋅(b−a)⟹|a+b|2+|b−a|2=2a⋅a+2b⋅b=2(|a|2+|b|2)

which makes our assumption that the law is true absolutely true.

hope it helps..!!!!❤