If a- b- and c- are unit vectors satisfying -a-b-2-b-c-2-c-a-2-9- then -2a-5b-5c- is

Given that, | a #160; b|^2 + | b #160; c|^2 + | c #160; a|^2 = 9 2( a^2 + b^2 + c^2 #160; ) 2( a b + b c + c a #160; ) =9 ...

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Applications of Dot Product

If a⃗, b⃗ a...

Question

If $\to a, \to b$ and $\to c$ are unit vectors satisfying $| \to a - \to b |^{2} + | \to b - \to c |^{2} + | \to c - \to a |^{2} = 9$ , then $| 2 \to a + 5 \to b + 5 \to c |$ is

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\to a, \to b,

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(\to a \times \to b) . (\to b \times \to c) + (\to b \times \to c) . (\to c \times \to a) + (\to c \times \to a) . (\to a \times \to b)

\to a, \to b

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\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(\to a + \to b) \cdot \to p + (\to b + \to c) \cdot \to q + (\to c + \to a) \cdot \to r =

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[\to a + \to b + \to c \to a + \to b \to a + \to c] = - [\to a \to b \to c]

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| \to a + \to b + \to c |

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