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 $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}$ If $\vec{b}$ and $\vec{c}$ are non-parallel, then the value of $λ$ is

Question

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  $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}$ If  $\vec{b}$  and  $\vec{c}$  are non-parallel, then the value of  $λ$  is

cdquestions Admin · Accepted Answer

$\vec{a} = 3\hat{i} + \hat{j} \quad \text{and} \quad \vec{b} = \hat{i} + 2\hat{j} + \hat{k}$ $\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c} = \vec{b} + \lambda \vec{c}$ If  $\vec{b} \quad \text{and} \quad \vec{c}$   are non-parallel, then $\vec{a} \cdot \vec{c} = 1 \quad \text{and} \quad \vec{a} \cdot \vec{b} = -\lambda$ but  $\vec{a} \cdot \vec{b} = 5$ $⇒λ=−5$ So, the correct option is (A): -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 \(\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}\)
If \(\vec{b}\) and \(\vec{c}\) are non-parallel, then the value of \(λ\) is

The Correct Option is A

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Vector Algebra

Vector Algebra Operations:

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 \(\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}\)If \(\vec{b}\) and \(\vec{c}\) are non-parallel, then the value of \(λ\) is