If a- b- c- are unit vectors such that a-b-c-0- then the value of a-b-b-c-c-a- is equal to

The correct option is C 3/2Given that nbsp;a+b+c=0 ⇒ |a+b+c|^2=0 ⇒ 3+2(a·b+b·c+c·a)=0 ⇒a·b+b·c+c·a= 3/2 ...

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Byju's Answer

Standard XII

Physics

Unit Vectors

If a⃗, b⃗, c⃗...

Question

If $\to a, \to b, \to c$ are unit vectors such that $\to a + \to b + \to c = \to 0,$ then the value of $\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a$ is equal to

1

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3

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\frac{3}{2}

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- \frac{3}{2}

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Solution

The correct option is D $- \frac{3}{2}$
Given that $\to a + \to b + \to c = \to 0$

$\Rightarrow | \to a + \to b + \to c |^{2} = 0$

$\Rightarrow 3 + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 0$

$\Rightarrow \to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a = - \frac{3}{2}$

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Similar questions

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_____

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If →a,→b,→c are unit vectors such that →a+→b+→c=→0, then the value of →a⋅→b+→b⋅→c+→c⋅→a is equal to

The correct option is D −32Given that →a+→b+→c=→0 ⇒|→a+→b+→c|2=0 ⇒3+2(→a⋅→b+→b⋅→c+→c⋅→a)=0 ⇒→a⋅→b+→b⋅→c+→c⋅→a=−32

If $\to a, \to b, \to c$ are unit vectors such that $\to a + \to b + \to c = \to 0,$ then the value of $\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a$ is equal to