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Question regarding vectors.

  1. Jul 2, 2012 #1
    1. The problem statement, all variables and given/known data

    The x and y components of vector P have numerical values 6 and 6 , respectively , and that of P + Q have numerical values 10 and 9. What are the numerical values of x and y components of vector Q ?

    Note this problem gave the following values :

    |Px| = 6
    |Py|=6
    |P + Q| = 10 or 9
    |Qx| = ? To find..
    |Qy|=? To find...

    2. Relevant equations

    |P + Q|2 = P2 + Q2
    +2PQcosθ

    Here |P| = P
    |Q| = Q

    3. The attempt at a solution

    ( Px = Py = 6)

    P2 = Px2 + Py2
    P2 = 72
    P = 6√2

    |P + Q|2 = P2 + Q2
    +2PQcosθ

    Putting P= 6√2
    and

    |P + Q| = 10 (given)

    and also |P + Q| = 9 (given)

    I get two equations :

    Q2 + 12√2 Qcosθ = 28
    Q2 + 12√2 Qcosθ = 9

    Now what ??? How will I proceed ? :confused:

    Thanks in advance... :smile:
     
  2. jcsd
  3. Jul 2, 2012 #2
    Hi sankalpmittal :smile:

    Why use such a long approach?? You can simply see that P vector is given as, [itex]\vec{P}=6i + 6j[/itex] and [itex]\vec{P}+\vec{Q}= 10i + 9j[/itex], where i, j are unit vectors in the respective directions...So what would vector Q be?
     
  4. Jul 3, 2012 #3
    The magnitude of x and y components of Q vector will be 4,3 !! That's what the answer given in the question booklet !!

    Thanks Infinitum !! :smile:

    Moral : Keep things simple.. :redface:
     
  5. Jul 3, 2012 #4
    Well, usually :wink:
     
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