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$| a | = | b | = | c | = | a + b + c | = 1$ and $a ⊥ b, (c, a) = α, (c, b) = β,$ $\cos α + \cos β =$

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answer is C.

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Detailed Solution

$a . b = 0, b . c = 1 \times 1 \times \cos β = \cos β c . a = 1 \times 1 \times \cos α = \cos α |a + b + c| = 1 \Rightarrow {|a + b + c|}^{2} = 1 \Rightarrow 1 + 1 + 1 + 2 (0 + \cos α + \cos β) = 1 \cos α + \cos β = \frac{1 - 3}{2} = - 1$

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