If a→,b→ and c→ are such that [a→b→c→]=1,c→=λ(a→×b)→ ,|a→|=2,|b→|=3 and |c→|=13, then the angle between a→ and b→ is

c→=λ(a→×b→) or c→⋅c→=λ(a→×b→)⋅c→⇒ 13=λ Also |c→|2=λ2|a→×b→|2⇒ 13=19a2b2sin2⁡θ=19×2×3sin2⁡θ or sin2⁡θ=12 or θ=π4

If a→,b→ and c→ are such that [a→b→c→]=1,c→=λ(a→×b)→ ,|a→|=2,|b→|=3 and |c→|=13, then the angle between a→ and b→ is

c→=λ(a→×b→) or c→⋅c→=λ(a→×b→)⋅c→⇒ 13=λ Also |c→|2=λ2|a→×b→|2⇒ 13=19a2b2sin2⁡θ=19×2×3sin2⁡θ or sin2⁡θ=12 or θ=π4

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$If \vec{a}, \vec{b} and \vec{c} are such that [\vec{a} \vec{b} \vec{c}] = 1, \vec{c} = λ (\vec{a} \times \vec{b)}, | \vec{a} | = \sqrt{2}, | \vec{b} | = \sqrt{3} and | \vec{c} | = \frac{1}{\sqrt{3}}, then the angle between \vec{a} and \vec{b} is$

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$\frac{π}{6}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{2}$

answer is B.

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Detailed Solution

$\vec{c} = λ (\vec{a} \times \vec{b})$

$or \vec{c} \cdot \vec{c} = λ (\vec{a} \times \vec{b}) \cdot \vec{c}$

$\Rightarrow \frac{1}{3} = λ$

$Also | \vec{c} |^{2} = λ^{2} | \vec{a} \times \vec{b} |^{2}$

$\Rightarrow \frac{1}{3} = \frac{1}{9} (a^{2} b^{2} \sin^{2} θ) = \frac{1}{9} \times 2 \times 3 \sin^{2} θ$

$or \sin^{2} θ = \frac{1}{2}$

$or θ = \frac{π}{4}$

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If a→,b→ and c→ are such that [a→b→c→]=1,c→=λ(a→×b)→ ,|a→|=2,|b→|=3 and |c→|=13, then the angle between a→ and b→ is

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$If \vec{a}, \vec{b} and \vec{c} are such that [\vec{a} \vec{b} \vec{c}] = 1, \vec{c} = λ (\vec{a} \times \vec{b)}, | \vec{a} | = \sqrt{2}, | \vec{b} | = \sqrt{3} and | \vec{c} | = \frac{1}{\sqrt{3}}, then the angle between \vec{a} and \vec{b} is$