Let a, →b →,c → be non-coplanar vectors such that a→×(b→×c→)=b→2, then the angle between a¯and b¯ is

a→×(b→×c→)=b→2⇒(a→⋅c→)b→−(a→⋅b→)c→=b→2⇒ a→⋅b→=0,a→⋅c→=12 ∴ a→⊥b→

Let a, →b →,c → be non-coplanar vectors such that a→×(b→×c→)=b→2, then the angle between a¯and b¯ is

a→×(b→×c→)=b→2⇒(a→⋅c→)b→−(a→⋅b→)c→=b→2⇒ a→⋅b→=0,a→⋅c→=12 ∴ a→⊥b→

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Let $\vec{a,} \vec{b}, \vec{c}$ be non-coplanar vectors such that
$\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b}}{2}$ , then the angle between $\bar{a} a n d \bar{b}$ is

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$π$

$\frac{3 π}{4}$

$\frac{π}{4}$

$\frac{π}{2}$

answer is C.

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$\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b}}{2} \Rightarrow (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} = \frac{\vec{b}}{2}$

$\Rightarrow \vec{a} \cdot \vec{b} = 0, \vec{a} \cdot \vec{c} = \frac{1}{2} ∴ \vec{a} ⊥ \vec{b}$

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Let a, →b →,c → be non-coplanar vectors such that a→×(b→×c→)=b→2, then the angle between a¯and b¯ is

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Let $\vec{a,} \vec{b}, \vec{c}$ be non-coplanar vectors such that
$\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b}}{2}$ , then the angle between $\bar{a} a n d \bar{b}$ is