ABCDEF is a regular hexagon with sides of unit length. Find the magnitude and the direction of AB+AC+AD+AE+AF.

The textbook answer: 6, 60 degrees to AB

A full solution with steps will be greatly appreciated.
Thank you :)

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  2. I put A at lower left and B a lower right.
    AB = 1 i + 0 j
    AC = (1+cos 60)i + sin 60 j
    AD = 1 i + 2 sin 60 j
    AE = 0 i + 2 sin 60 j
    AF = -cos 60 i + sin 60 j
    sum of x components = 3
    sum of y components = 6 sin 60 = 6 (sqrt3 /2) = 3 sqrt 3
    magnitude = sqrt(3^2 + 9*3) = sqrt 36 = 6 sure enough
    tan angle = sqrt 3 /1
    so angle = 60

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