I really couldn't find anything related to this simple identity I came up with so: r → = ( r x , r y ) = ( r x , ∠ 0 ) + ( r y , ∠ π 2 )My thinking process was that r y is practically the modulus of a vector in the Y axis (or with θ = 90 ° = π 2 ) and r x is the modulus of a vector in the X axis (or with θ = 0 ° = 0).Is this true?

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I really couldn&#039;t find anything related to this simple identity I came up with so:            r      →        =  (      r    x    ,      r    y    )  =  (      r    x    ,  ∠  0  )  +  (      r    y    ,  ∠      π    2    )My thinking process was that       r    y   is practically the modulus of a vector in the Y axis (or with   θ  =  90      °    =      π    2  ) and       r    x   is the modulus of a vector in the X axis (or with   θ  =  0      °    =  0).Is this true?

Audrey Russell · Accepted Answer

The statement            r      →        =  (      r    x    ,      r    y    )  =  (      r    x    ,  ∠  0  )  +  (      r    y    ,  ∠      π    2    )Is equivalent to the statement that      r    =      [                                        r            1                                                            r            2                                ]    =      r    1        [                            1                                      0                      ]    +      r    2        [                            0                                      1                      ]    =      r    1                      i        ^              +      r    2                      j        ^            where                     i        ^             and                     j        ^             are the standard basis of             R        2  . You will note that any n-dimensional vector can be expressed as a linear combtination of some n independent basis vectors. In fact, each component       v    i   of a vector can be conceptulized as the factor by which the ith basis vector of a vector space must be scaled when producing the vector.This property is true for greater dimensions that 2, and can be extended to vector spaces besides             R        n  . This concept is fundamental to understanding linear algebra. Matrices, for instance, can be understood as linear transformations of space, where the ith column of the matrix describes where the ith basis vector &quot;lands&quot; after moving through the transformation.

I really couldn't find anything related to this simple identity I came up with so: vec(r) =(r_x,r_y)=(r_x,/_0)+(r_y, /_ pi/2)

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