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Summary

a⃗;b⃗;c⃗ are ...

Question

$\to a; \to b; \to c$ are three vectors so that each one is perpendicular to the sum of the other two and also $| \to a | = 40; | \to b | = 20; | \to c | = 4$ then $| \to a + \to b + \to c | +$ .......

2016

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2015

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\sqrt{2016}

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\sqrt{2015}

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Solution

The correct option is C $\sqrt{2016}$
$| \to a | = 40; | \to b | = 20; | \to c | = 4$
$\to a$ is $⊥$ to $\to b + \to c$
$\to a, (\to b + \to c) 20 \Rightarrow \to a . \to b + \to a . \to b = 0$ ......... $(1)$
Similarly
$\to b . (\to a + \to c) \Rightarrow \to b . \to a + \to b . \to c = 0$ ............... $(2)$
$\to c . (\to a + \to b) \Rightarrow \to c . \to a + \to c . \to b = 0$ ............ $(3)$
$| \to a + \to b + \to c |^{2} = \to a .^a +^a . \to b +^a . \to c +^b . \to a +^b . \to b +^b . \to c + \to c .^a + \to c .^b + \to c .^c$
$\Rightarrow | \to a |^{2} + | \to b |^{2} + | \to |^{2} + (\to a . \to b + \to a . \to c) + (\to b . \to a + \to b .^c) + (\to c . \to a + \to c .^a)$
(From $(1), (2)$ & $(3)$ we get)
$\Rightarrow | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 0$
$\Rightarrow (40)^{2} + (20)^{2} + 4^{2} + 0$
$\Rightarrow 1600 + 400 + 16 = 2016$
$|^a +^b +^c | = \sqrt{2016}$
$∴$ Option $C$ is correct

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