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Physics · MOTION IN A PLANE
हिन्दीIf \( |\mathbf{A}| = 3 \), \( |\mathbf{B}| = 4 \), and the magnitude of their sum is \( |\mathbf{A} + \mathbf{B}| = 5 \), evaluate the magnitude of the vector linear combination \( |\mathbf{A} - 2\mathbf{B}| \).
Correct answer · Option 4
\( \sqrt{73} \)
Explanation
Since \( 3^2 + 4^2 = 5^2 \), vectors \( \mathbf{A} \) and \( \mathbf{B} \) are orthogonal (\( \mathbf{A} \perp \mathbf{B} \)). Therefore, \( |\mathbf{A} - 2\mathbf{B}|^2 = |\mathbf{A}|^2 + 4|\mathbf{B}|^2 = 3^2 + 4(4^2) = 9 + 64 = 73 \implies |\mathbf{A} - 2\mathbf{B}| = \sqrt{73} \).
