Question

$\displaystyle{\red{Question:-}}$
What is Commutative law ,prove that addition vectors obeys it.

class - 11 , Subject - Physics
Topic - Vectors

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Answer 1

Answer:

The Commutative law states that the order of addition doesn't matter, that is : A+B is equal to B+A. 2 The Associative law, which states that the sum of three vectors does not depend on which pair of vectors is added first, that is: (A+B)+C=A+(B+C).

Answer 2

$\mathtt{\green{Answer:-}}$

$\underline{\bold{Commutative \: Law :-}}$

If the order of addition of two vectors is reversed then, their resultant " Vectors remains unchanged "

$\underline{\bold{Proof:-}}$

$\red{\bigstar}$in the figure (see attachment)

In ∆OAB by ∆-law of Vector addition

$\bold{\overrightarrow{OB} = \overrightarrow{OA} + \overrightarrow{AB}}$

$\boxed{\bold{\overrightarrow{OB}=\overrightarrow{a} +\overrightarrow{b}}}$ ---(1)

And in ∆OCB by ∆-law of vector addition

$\bold{\overrightarrow{OB} = \overrightarrow{OC} + \overrightarrow{CB}}$

$\boxed{\bold{\overrightarrow{OB}=\overrightarrow{b} +\overrightarrow{a}}}$ ---(2)

Now, Value Putting in equation 2 from 1

$:\implies\boxed{\underline{\mathtt{\green{\overrightarrow{a} +\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}}}}}$

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What is ∆ law of vector addition?

if two vector acting on a particle are represented by the two sides of a triangle in the same order then their resultant vector is completely represented by the third side of triangle taken in opposite order.

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