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Vectors and magnitudes

  1. Jan 9, 2014 #1
    1. The problem statement, all variables and given/known data

    Vector A has magnitude 3 and points to the right. Vector B has magnitude 4 and points vertically upwards. Find the magnitude of vector C such that A + B + C = 0


    3. The attempt at a solution

    C = SQRT[4^2 + 5^2] = 6.4
     
  2. jcsd
  3. Jan 9, 2014 #2

    SteamKing

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    Draw a picture.
     
  4. Jan 9, 2014 #3

    CWatters

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    What SteamKing said. It's not 6.4
     
  5. Jan 9, 2014 #4
    Where did the "5" come from?
     
  6. Jan 9, 2014 #5
    Very good idea to draw a picture as SteamKing said.

    Another approach is to express the direction of the vectors with ##\hat{i}## and ##\hat{j}## components, where ##\hat{i}## represents the x-direction of the vector and ##\hat{j}## represents the y-direction of the vector.

    Here is the concrete demonstration of the vectors: if a vector points to the right, then we obtain the positive ##\hat{i}## component. If a vector points up, then we obtain the positive ##\hat{j}## component. From here, we see that if a vector points up and right, then we obtain both positive ##\hat{i}## and ##\hat{j}## components.

    Remember, when combining vectors, you have to add their magnitudes component-wise as you do with variables in pre-calculus class.

    Note: The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector ##\vec{C}## in which ##\vec{A} + \vec{B} + \vec{C} = 0##
     
  7. Jan 9, 2014 #6
    It should be 3^2. Careless blunder
     
  8. Jan 9, 2014 #7
    Capture.JPG
     
  9. Jan 9, 2014 #8
    Your C vector has two heads. It should only have one. Which one do you judge is the correct one?
    Chet
     
  10. Jan 9, 2014 #9
    The correct one points to the left.
     
  11. Jan 9, 2014 #10
    The vector ##\vec{C}## does NOT point to the right. As I mentioned before:

    The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector ##\vec{C}## in which ##\vec{A} + \vec{B} + \vec{C} = 0##

    Good. Also, which ##y##-direction is the vector ##\vec{C}## pointing at? Remember that its direction is opposite to the combination of the two vectors ##\vec{A}## and ##\vec{B}##, which points up-right. The vector ##\vec{C}## does not only point to the left. It also points... (You figure out the y-direction)
     
  12. Jan 9, 2014 #11
    It also points downwards. It is in the direction -j hat
     
  13. Jan 9, 2014 #12
    Nicely done. ;) Finally, determine the magnitude of ##\vec{C}##, and you are done.
     
  14. Jan 10, 2014 #13
    Magnitude of c = 5
     
  15. Jan 10, 2014 #14

    BruceW

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    yep :)
     
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