Math

These are vectors as well:
(a) AB + __ = CA = 0

(b) AB +BC + CD + DA = __
the first was a mistake i wanted these ones. Complete these and please if you can, explain.

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  1. Looks to me like

    AB + BC + CA = 0
    Similarly for the other one. Getting back to A, the sum is just 0 again.

    The vectors form a closed polygon, so the net result is zero.

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    posted by Steve
  2. If you want to use vector notation, then if the vector to A is a, and to B is b, etc.

    Then

    AB = b-a
    BC = c-b
    CA = a-c

    AB+BC+CA = b-a+c-b+a-c = 0

    AB is b-a because if there is a vector u such that a+u=b, then u=b-a.

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    posted by Steve
  3. Thanks this will help.
    I only knew of:
    AB + BC = AC(triangle rule)
    and
    AB + BC + CD = AC + CD = AD(parallelgram rule)

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