If a- b- c- are three unit vectors- a- b-c- -1-2b- then angle between a and c is

The correct option is B π /3 Given, #160; a⃗× ( b⃗×c⃗ ) = 12b⃗ ⇒ (a· c)b⃗ (a· b) c⃗ = 12b⃗ Comparing coefficient of b⃗ , a⃗·c⃗ ...

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Byju's Answer

Standard XII

Physics

Angular Velocity

If a⃗, b⃗...

Question

If $\to a$ , $\to b$ , $\to c$ are three unit vectors, $\to a \times (\to b \times \to c) = \frac{1}{2} \to b,$ then angle between a and c is

π / 6

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π / 2

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π / 3

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None of these

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Solution

The correct option is B $π / 3$
Given, $\to a \times (\to b \times \to c)$ $= \frac{1}{2} \to b$
$\Rightarrow (a \cdot c) \to b - (a \cdot b) \to c = \frac{1}{2} \to b$
Comparing coefficient of $\to b$ ,
$\to a \cdot \to c = \frac{1}{2} \Rightarrow | a | | c | cos θ = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$
Hence angle between $a$ and $c$ is $\frac{π}{3}$

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Similar questions

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If →a, →b, →c are three unit vectors, →a×(→b×→c)=12→b, then angle between a and c is

The correct option is B π/3Given, →a×(→b×→c) =12→b⇒(a⋅c)→b−(a⋅b)→c=12→bComparing coefficient of →b,→a⋅→c=12⇒|a||c|cosθ=12⇒θ=π3Hence angle between a and c is π3

If $\to a$ , $\to b$ , $\to c$ are three unit vectors, $\to a \times (\to b \times \to c) = \frac{1}{2} \to b,$ then angle between a and c is