Question:medium
Let the vectors \( \mathbf{a} = -\hat{i} + \hat{j} + 3\hat{k} \) and \( \mathbf{b} = \hat{i} + 3\hat{j} + \hat{k} \). For some \( \lambda, \mu \in \mathbb{R} \), let \( \mathbf{c} = \lambda \mathbf{a} + \mu \mathbf{b} \). If \( \mathbf{c} \cdot (3\hat{i} - 6\hat{j} + 2\hat{k}) = 10 \) and \( \mathbf{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = -2 \), then \( |\mathbf{c}|^2 \) is equal to:
Let the vectors \( \mathbf{a} = -\hat{i} + \hat{j} + 3\hat{k} \) and \( \mathbf{b} = \hat{i} + 3\hat{j} + \hat{k} \). For some \( \lambda, \mu \in \mathbb{R} \), let \( \mathbf{c} = \lambda \mathbf{a} + \mu \mathbf{b} \). If \( \mathbf{c} \cdot (3\hat{i} - 6\hat{j} + 2\hat{k}) = 10 \) and \( \mathbf{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = -2 \), then \( |\mathbf{c}|^2 \) is equal to:
Updated On: Apr 10, 2026
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The Correct Option is C
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