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Can a dot product be negative in case of length?

  1. Apr 12, 2014 #1
    Let's say A and B are 2 vectors with length in cm and the angle between them is 170°.

    Obviously, the dot product of A and B will give cm2 as unit but since the value of cos(170) is negative, will the dot product be negative (something)cm2?
  2. jcsd
  3. Apr 12, 2014 #2


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    Yes, the dot product will be negative. The geometric implication is that when A is projected onto B, the projection will be in the opposite direction to B (and vice versa).

    The length merely represents the magnitude of a vector, and not its direction. A length is always non-negative, but that doesn't stop the dot product of two vectors from being negative.
    Last edited: Apr 12, 2014
  4. Apr 12, 2014 #3
    Aha! Thanks.
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