Let a→=3i^+j^ and b→=i^+2j^+k^. Let c→be a vector satisfying a→×(b→×c→)=b→+λc→. If b→ and c→are non-parallel, then the value of λ is :

a→=3i^+j^,b→=i^+2j^+k^ Given, a→×(b→×c→)=b→+λc→⇒(a→⋅c→)b→−(a→⋅b→)c→=b→+λc→ ⇒a→⋅c→=1,a→⋅b→=−λ⇒(3i^+j^)⋅(i^+2j^+k^)=−λ⇒(3+2+0)=−λ⇒λ=−5

Let a→=3i^+j^ and b→=i^+2j^+k^. Let c→be a vector satisfying a→×(b→×c→)=b→+λc→. If b→ and c→are non-parallel, then the value of λ is :

a→=3i^+j^,b→=i^+2j^+k^ Given, a→×(b→×c→)=b→+λc→⇒(a→⋅c→)b→−(a→⋅b→)c→=b→+λc→ ⇒a→⋅c→=1,a→⋅b→=−λ⇒(3i^+j^)⋅(i^+2j^+k^)=−λ⇒(3+2+0)=−λ⇒λ=−5

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Let $\vec{a} = 3 \hat{i} + \hat{j} and \vec{b} = \hat{i} + 2 \hat{j} + \hat{k}$ . Let $\vec{c}$ be a vector satisfying $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + λ \vec{c}$ . If $\vec{b} and \vec{c}$ are non-parallel, then the value of $λ$ is :

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Detailed Solution

$\vec{a} = 3 \hat{i} + \hat{j}, \vec{b} = \hat{i} + 2 \hat{j} + \hat{k} Given, \vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + λ \vec{c} \Rightarrow (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} = \vec{b} + λ \vec{c} \begin{array}{l} \Rightarrow \vec{a} \cdot \vec{c} = 1, \vec{a} \cdot \vec{b} = - λ \Rightarrow (3 \hat{i} + \hat{j}) \cdot (\hat{i} + 2 \hat{j} + \hat{k}) = - λ \\ \Rightarrow (3 + 2 + 0) = - λ \Rightarrow λ = - 5 \end{array}$