Question:medium
Let \( \vec{a} = \hat{i} - 2\hat{j} + 3\hat{k} \). If \( \vec{b} \) is a vector such that \( \vec{a} \cdot \vec{b} = |\vec{b}|^2 \) and \( |\vec{a} - \vec{b}| = \sqrt{7} \), then \( |\vec{b}| = \)
Let \( \vec{a} = \hat{i} - 2\hat{j} + 3\hat{k} \). If \( \vec{b} \) is a vector such that \( \vec{a} \cdot \vec{b} = |\vec{b}|^2 \) and \( |\vec{a} - \vec{b}| = \sqrt{7} \), then \( |\vec{b}| = \)
Show Hint
Whenever magnitude and dot product are both given, expand \( |\vec{a}\pm\vec{b}|^2 \) first. It simplifies the problem quickly.
Updated On: May 6, 2026
- \( \sqrt{7} \)
- \( \sqrt{3} \)
- \( 7 \)
- \( 3 \)
- \( 7\sqrt{3} \)
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The Correct Option is A
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