Question:
For two vectors $ \mathbf{A} $ and $ \mathbf{B} $, if $ \mathbf{A} + \mathbf{B} = |\mathbf{A} - \mathbf{B}| $, then
For two vectors $ \mathbf{A} $ and $ \mathbf{B} $, if $ \mathbf{A} + \mathbf{B} = |\mathbf{A} - \mathbf{B}| $, then
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In vector questions involving equality of magnitudes, check the condition of perpendicularity first when the equation involves the difference of the vectors.
Updated On: May 9, 2025
- \( \mathbf{A} \) and \( \mathbf{B} \) are parallel vectors.
- \( \mathbf{A} \) and \( \mathbf{B} \) are opposite vectors.
- \( \mathbf{A} \) and \( \mathbf{B} \) are perpendicular to each other.
- Angle between \( \mathbf{A} \) and \( \mathbf{B} \) is \( 120^\circ \).
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The Correct Option is C
Solution and Explanation
The equation \( \mathbf{A} + \mathbf{B} = |\mathbf{A} - \mathbf{B}| \) implies that the vectors \( \mathbf{A} \) and \( \mathbf{B} \) are perpendicular. This can be shown by applying the Pythagorean theorem to the vector magnitudes and realizing that the sum of squares of the magnitudes of the vectors on both sides must be equal. This condition is satisfied only when the vectors are perpendicular.
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