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Math Help - Vectors: simplify equation.

  1. #1
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    Vectors: simplify equation.

    Simplify equation (all are vectors):
    (XY - YZ) - (ZT + XT) + (ZY - ZT)
    The given answer is 3TY, but I don't know how to get that answer. Please help. For example I'd say that XY - YZ = -YX - YZ = ZX, but that's not TY... Then I'd say ZT - XT = -ZT + XT = ZX(also not TY), then ZY - ZT = TY. So that would be ZX - ZX + TY = TY (not 3TY)
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  2. #2
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    Quote Originally Posted by Evaldas View Post
    Simplify equation (all are vectors):
    (XY - YZ) - (ZT + XT) + (ZY - ZT)
    The given answer is 3TY, but I don't know how to get that answer. Please help. For example I'd say that XY - YZ = -YX - YZ = ZX, but that's not TY... Then I'd say ZT - XT = -ZT + XT = ZX(also not TY), then ZY - ZT = TY. So that would be ZX - ZX + TY = TY (not 3TY)
    Step 1. Get rid of the parentheses: XY – YZ – ZT – XT + ZY – ZT.

    Step 2. Get rid of all the minus signs, using the fact that –AB = BA.

    Step 3. Group the six vectors into three pairs and combine each pair into a single vector, using the fact that AB + BC = AC (you'll have to rearrange the order of the six vectors to get them to pair up properly).
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  3. #3
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    One method is to represent every vector in this expression as the difference of two vectors with the beginning at the origin O. E.g., XY = OY - OX, ZT = OT - OZ, etc. Then one has to add like terms to get 3OY - 3OT = 3TY.
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  4. #4
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    Done! Thank you very much!
    XY + ZY + TZ + TX + ZY + TZ = (TZ + ZY) + (TX + XY) + (TZ + ZY) = TY + TY + TY = 3TY.
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