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Applications of Dot Product

If a, b, c ...

Question

If $\to a, \to b, \to c$ are unit vectors such that $\to a + \to b + \to c = 0$ , find the value of $\to a . \to b + \to b . \to c + \to c . \to a$ .

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Solution

$\to a + \to b + \to c = 0 N o w t a k e t h e d o t p r o d u c t o f t h i s w i t h i t s e l f w e g e t | a |^{2} + | b |^{2} + | c |^{2} + 2 (\to a . \to b + \to b . \to c + \to c . \to a) = 0 \to a . \to b + \to b . \to c + \to c . \to a = \frac{- 3}{2}$

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