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Addition of Vectors

a⃗ and b⃗ f...

Question

$\to a$ and $\to b$ form the consecutive sides of a regular hexagon ABCDEF.
$\to A B = \to a, \to B C = \to b$

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Solution

$\to A B = \to a, \to B C = \to b$
$\to A C = \to A B + \to B C = \to a + \to a$ (i)
$\to A D = 2 \to B C = 2 \to b$ (ii)
(because AD is parallel to BC and twice its length).
$\to C D = \to A D - \to A C = 2 \to b - (\to a + \to b) = \to b - \to a$
$\to F A = - \to C D = \to a - \to b$ (iii)
$\to D E = - \to A B = - \to a$ (iv)
$\to E F = - \to B C = - \to b$ (v)
$\to A E = \to A D + \to D E = 2 \to b - \to a$ (vi)
$\to C E = \to C D + \to D E = \to b - \to A - \to A = \to b - 2 \to a$ (vii)

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