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Vector basics

  1. Aug 23, 2007 #1
    1. The problem statement, all variables and given/known data

    I have two vectors V1 and V2.
    V1 is parallel to xz plane
    V2 is perpendicular to V1
    V2 is 10 units.Can i get V1?

    2. Relevant equations



    3. The attempt at a solution

    Force triangle?Can''t solve?
     
  2. jcsd
  3. Aug 23, 2007 #2
    You can only get V1's direction, not magnitude.
     
  4. Aug 23, 2007 #3
    How can we get the direction of V1?
     
  5. Aug 23, 2007 #4

    Dick

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    The normal to the xz plane is the vector V3=(0,1,0). If V1 is parallel to the xz plane then it is perpendicular to V3. So V1 is perpendicular to V2 and V3. So a direction for V1 is given by the vector cross product of V2xV3.
     
  6. Aug 23, 2007 #5
    But from the given conditions, v2 (only the magnitude is known) is not given, how can you know v1's direction ?
     
  7. Aug 23, 2007 #6

    Dick

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    The direction is the same as v2x(0,1,0). That's about all you can say. And if v2 is parallel to (0,1,0) then you can't say much of anything at all.
     
  8. Aug 23, 2007 #7
    You said:
    what will be the value of cross product V2 x V3?
     
  9. Aug 23, 2007 #8
    My question:

    what will be the value of cross product V2 x V3?
     
  10. Aug 23, 2007 #9

    Dick

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    Ok, shorter answer. NO. You can't 'get' V1.
     
  11. Aug 23, 2007 #10
    But what will be the cross product V2 x V3, in an expression?
     
  12. Aug 23, 2007 #11

    Dick

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    If V2=(x,y,z), (x,y,z)x(0,1,0)=(-z,0,x) (look up cross product). The result is in the xz plane is perpendicular to V2.
     
  13. Aug 24, 2007 #12
    Plz help with another case:

    1. If V2 and V3 are parallel
    2. Hence V1 = the cross product of V2 x V3 evaluates to 0,0,0
    3. What is the physical reason for this?
     
  14. Aug 24, 2007 #13

    Dick

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    The cross product is related to the area of the parallelogram created by the two vectors. What happens if they are parallel?
     
  15. Aug 24, 2007 #14
    Straight line?
     
  16. Aug 24, 2007 #15

    Dick

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    If you mean what I think you mean then yes. The area is zero. So the vector is zero.
     
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