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    Equilateral Triangle: Vectors

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    See the attachment for a diagram of an equilateral triangle with sides u, v and w. U is a unit vector. Find u dot v and u dot w (u.v and u.w).

    The answers are: u.v = 1/2, and u.w = -1/2.

    Why is u.w a minus 1/2?

    © BrainMass Inc. brainmass.com October 10, 2019, 3:56 am ad1c9bdddf
    https://brainmass.com/math/vector-calculus/equilateral-triangle-vectors-442499

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    From the diagram we see that:

    u + w = v

    Then:

    w = v - u

    And:

    u.w = u.(v-u)

    Because the dot product is distributive:

    u.w = u . (v-u) = u.v - u.u

    We know ...

    Solution Summary

    The solution finds u dot v and u dot w (u.v and u.w) from the diagram provided.

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