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Homework Help: A question about how vector direction affects equations

  1. Oct 13, 2016 #1
    • New member warned that the homework template must be used
    Hi there,

    I have a very basic maths problem that has highlighted a hole in my knowledge. I was answering the following question:

    The vertices of a triangle are A, B, C, with position vectors a, b, c . Show that the area of the triangle ABC is 1/2|b×c+c×a+a×b|.

    and got the answer as 1/2|(a*c) + (-a*b) + (-b*c)|

    I know that a*c = -c*a

    but that would mean when I attempt to get the answer given in the question by switching the letters so it reads:

    1/2|(-c*a) + (-a*b) + (-b*c)| i have a load of minus values in there? because i'm taking the modulus shown by the | on either side, does this mean I can just ignore the minus signs?

    cheers for your help!

  2. jcsd
  3. Oct 13, 2016 #2


    Staff: Mentor

    Presumably you mean a X c = -c X a, and similar for the area formula you show. There are three different kinds of multiplication for vectors in R3: the cross product (denoted with X), the dot product (denoted with ##\cdot##), and multiplication of a vector by a scalar, as in ##c\vec{v}##. To avoid confusion in readers, use the standard notation for the cross product.
    I don't think so. Since all your vector products point in the opposite direction, as compared to the answer you showed above, I suspect that you did something wrong in your calculation. Please show how you got this result.
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