If a- b- c- are unit vectors such that a-b-c-0- find the value of a-b-b-c-c-a-

We have |a⃗|=1, |b⃗|=1, |c⃗|=1 Also a⃗+b⃗+c⃗=0⃗ Squaring we get, #160; |a⃗|^2+|b⃗|^2+|c⃗|^2+2(a⃗· #160;b⃗+b⃗· #160;c⃗+c⃗· #160;a⃗)=0 ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

If a⃗, b⃗, ...

Question

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

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Solution

We have $| \to a | = 1, | \to b | = 1, | \to c | = 1$

Also $\to a + \to b + \to c = \to 0$

Squaring we get,

$| \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 0$

$\Rightarrow 1 + 1 + 1 + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 0$

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

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Similar questions

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\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a =

_____

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$I f \to a, \to b \to c a r e u n i t v e c t o r s s u c h t h a t \to a + \to b + \to c = \to 0, t h e n t h e v a l u e o f \to a . \to b + \to b . \to c + \to c . \to a i s$

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If →a,→b,→c are unit vectors such that →a+→b+→c=→0, find the value of →a⋅→b+→b⋅→c+→c⋅→a

We have |→a|=1,|→b|=1,|→c|=1Also →a+→b+→c=→0Squaring we get, |→a|2+|→b|2+|→c|2+2(→a⋅→b+→b⋅→c+→c⋅→a)=0⇒1+1+1+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 $\to a + \to b + \to c = \to 0$ , find the value of $\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a$