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Math Help - Vectors p and q

  1. #1
    Member u2_wa's Avatar
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    Vectors p and q

    There are two coplanar vectors p & q. If ap+bq=0 (scalar multiplication), what can be inferred about the values of a & b?

    In my view answer should be a=b=0 but how about if p and q are also parallel!
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  2. #2
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    Hello u2_wa
    Quote Originally Posted by u2_wa View Post
    There are two coplanar vectors p & q. If ap+bq=0 (scalar multiplication), what can be inferred about the values of a & b?

    In my view answer should be a=b=0 but how about if p and q are also parallel!
    You are right: if \vec p and \vec q are non-zero, non-parallel vectors then a = b = 0.

    If \vec p and \vec q are parallel, then, for some \lambda:
    \vec p =\lambda \vec q

    i.e. \vec p -\lambda\vec q = \vec 0 (note: a zero vector)

    In which case, all you can say is that, for this value of \lambda, \;a:b = -1:\lambda.

    If \vec p= \vec 0, and \vec q \ne \vec 0, then a\vec p + b\vec q = \vec 0 \Rightarrow b = 0 and a can take any value.

    Similarly if \vec p\ne \vec 0, and \vec q = \vec 0, then a\vec p + b\vec q = \vec 0  \Rightarrow a = 0 and b can take any value.

    I think that just about covers all possible cases.

    Grandad
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