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Homework Help: Vector components question?

  1. Jul 31, 2014 #1
    "Is it possible for a vector that has nonzero magnitude to have a component in some direction that is equal to zero?"
    The answer key said that any vector that has a nonzero magnitude will always have a component of zero length in the direction perpendicular to the vector.

    I'm having trouble visualizing this. Why will the vector always have a component of zero length?
    If anyone could break this down for me it would be much appreciated!
  2. jcsd
  3. Jul 31, 2014 #2


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    Staff: Mentor

    Imagine a vector rising perpendicularly from a line (any given line). What's the projection of that vector onto the line?

    An obvious analogy is the x-y axes of the Cartesian plane. How much "y" lies along the direction of "x"?
  4. Jul 31, 2014 #3

    rude man

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    Homework Helper
    Gold Member

    Draw a vector A on paper. Now, draw a vector B perpendicular to the A vector, both A and B have their startying ends together. Now draw a vector C from the tip of A to the tip of B. You obviously have C = A + B. How small does B have to be so that A = C?
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