Question:medium
If \( \vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 4\hat{i} + 3\hat{j} + 4\hat{k} \) and \( \vec{c} = \hat{i} + \alpha \hat{j} + \beta \hat{k} \) are coplanar and \( |\vec{c}| = \sqrt{3} \), then
If \( \vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 4\hat{i} + 3\hat{j} + 4\hat{k} \) and \( \vec{c} = \hat{i} + \alpha \hat{j} + \beta \hat{k} \) are coplanar and \( |\vec{c}| = \sqrt{3} \), then
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Coplanarity ⇒ always use determinant = 0.
Updated On: May 8, 2026
- \( \alpha = \sqrt{2}, \beta = 1 \)
- \( \alpha = 1, \beta = \pm1 \)
- \( \alpha = \pm1, \beta = 1 \)
- \( \alpha = \pm1, \beta = -1 \)
- \( \alpha = -1, \beta = \pm1 \)
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The Correct Option is B
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