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Unit vector

  1. May 21, 2012 #1
    Our teacher taught us a way to represent a force as a unit vector.

    Suppose a force of 12 N acts along the line 2i+j-2k. The force is written as:

    F = 12 N (2i+j-2k/√1^2+2^2+2^2)


    F = 8i+4j-8k

    But, I can't understand why is it so. Please explain.
  2. jcsd
  3. May 21, 2012 #2


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    Science Advisor
    Homework Helper

    hi physics kiddy! :smile:

    let's take an easier 2D case, a force of 15 N acts along the line 3i + 4j

    if you draw 3i + 4j, you can see that it has magnitude 5

    so 3i + 4j represents a force of magnitude 5 N along that line

    to get a force of magnitude 15 N, we need 3 times that,

    = 3 N (3i + 4j)

    = 15 N (3i + 4j)/√(32 + 42)​

    the magnitude of the vector must equal the magnitude of the force, so we must always multiply the force by a unit vector …

    (ai + bj +ck)/√(a2 + b2 + c2) is always a unit vector :wink:
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