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Applications of Dot Product

Given that ...

Question

Given that $a = i + j + k; b = i - j + k; c = i + j - k$ evaluate $(a . b) + (b . c) + (c . a)$

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Solution

The correct option is A $1$
$(a . b) + (b . c) + (c . a) = (1 - 1 + 1) + (1 - 1 - 1) + (1 + 1 - 1) = 1 - 1 + 1 = 1$

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a = i + j + k; b = i - j + k; c = i + j - k

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