Let a-b- and c- be three unit vectors such that a- b-c- - -3-2 b- - c- is not parallel for the angle between a- and b- is

The correct option is B 5π/6 We have a #160; ×( b #160; ×c) = √(3)/2( b #160; + c) ( a .c)b #160; ( a .b)c #160; = √(3)/2b #160; + ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

Let a⃗,b⃗ a...

Question

Let $\to a, \to b$ and $\to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)$ is not parallel for the angle between $\to a$ and $\to b$ is

\frac{π}{2}

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\frac{2 π}{3}

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\frac{5 π}{6}

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\frac{3 π}{4}

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Solution

The correct option is B $\frac{5 π}{6}$
We have
$\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)$
$(\to a . \to c) \to b - (\to a . \to b) \to c = \frac{\sqrt{3}}{2} \to b + \frac{\sqrt{3}}{2} \to c$
We know that
$∵ ∣ ∣ \to a ∣ ∣ = ∣ ∣ ∣ \to b ∣ ∣ ∣ = ∣ ∣ \to c ∣ ∣ = 1$
$∴ \to a . \to b = \frac{\sqrt{3}}{2}$
$\Rightarrow cos θ = \frac{\sqrt{3}}{2}$
$∴ θ = \frac{5 π}{6}$
Hence, the option $C$ is the correct answer.

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Let →a,→b and →c be three unit vectors such that →a×(→b×→c)=√32(→b+→c) is not parallel for the angle between →a and →b is

The correct option is B 5π6We have→a×(→b×→c)=√32(→b+→c)(→a.→c)→b−(→a.→b)→c=√32→b+√32→cWe know that ∵∣∣→a∣∣=∣∣∣→b∣∣∣=∣∣→c∣∣=1∴→a.→b=√32⇒cosθ=√32∴θ=5π6Hence, the option C is the correct answer.

Let $\to a, \to b$ and $\to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)$ is not parallel for the angle between $\to a$ and $\to b$ is