Problem in Vector Resolution and Component

  1. I cannot understand what is vector resolution.It is said in the book that ON is the resolved part of A along X axis.It is also known as the x-component of A or the horizontal component of A.Ax may be regarded as the projection of A on X-axis. OM is the the resolved part of A along Y-axis.It is also known as the y-component of A or vertical component of A.The vertical component of A may be regarded as the projection of A on Y-axis.Now what is that projection? Is it the image of A on X-axis or Y axis?
    Then why Ax+Ay=A and not A=Ax or A=Ay?If Ax and Ay are the images of A on X and Y resp. then the magnitude of Ax and Ay should be same as A,but no, why? Please explain me.I am very much confused.
     

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  3. mathman

    mathman 6,437
    Science Advisor
    Gold Member

    If A = (a,b), then the x axis projection is (a,0) while the y axis projection is (0,b).

    It is quite simple - don't let the terminology confuse you.
     
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  4. vectors are simple

    Don't get muddled up. Let, me explain what projection is. Say, the vector extends from (0,0) to (a.b). Suppose, you want projection on the x-axis, take a light source and place it directly above the end of the vector, the shadow would be at (a,0). Thus the projection of the vector extends from (0,0) to (a,0). similarly, y-component would extend from (0,0) to (0,b).
    And, by the way Ax+Ay ≠ A. Using the Pythagoras theorem, (Ax)2+(Ay)2 = A2.
    What the book might have meant would have been, was vector Ax+vector Ay = vector A. By writing vector, I am also considering the direction. While, above, I was only talking about magnitudes. With a little practice, you would easily understand the difference between the vector and it's magnitude. So, good luck!!
     
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