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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीMatch List-I with List-II: List-I List-II A \( \vec{a} \times \vec{b} \) under coordinate reflection I \( -\vec{b} \times \vec{a} \) B Commutation of vector cross product II \( \vec{a} \times \vec{b} \) (does not change sign) C Vector product of parallel vectors \( \vec{a} \times \vec{a} \) III \( \vec{a} \times \vec{b} + \vec{a} \times \vec{c} \) D Distributive property \( \vec{a} \times (\vec{b} + \vec{c}) \) IV Null vector \( \vec{0} \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | \( \vec{a} \times \vec{b} \) under coordinate reflection | I | \( -\vec{b} \times \vec{a} \) |
| B | Commutation of vector cross product | II | \( \vec{a} \times \vec{b} \) (does not change sign) |
| C | Vector product of parallel vectors \( \vec{a} \times \vec{a} \) | III | \( \vec{a} \times \vec{b} + \vec{a} \times \vec{c} \) |
| D | Distributive property \( \vec{a} \times (\vec{b} + \vec{c}) \) | IV | Null vector \( \vec{0} \) |
Choose the correct answer from the options given below:
Correct answer · Option 1
A-(II), B-(I), C-(IV), D-(III)
Explanation
Under reflection \( \vec{a} \to -\vec{a}, \vec{b} \to -\vec{b} \implies \vec{a} \times \vec{b} \to \vec{a} \times \vec{b} \) (A-II). Anti-commutative: \( \vec{a} \times \vec{b} = -\vec{b} \times \vec{a} \) (B-I). Self cross product is zero: \( \vec{a} \times \vec{a} = \vec{0} \) (C-IV). Distributive rule: \( \vec{a} \times (\vec{b} + \vec{c}) = \vec{a} \times \vec{b} + \vec{a} \times \vec{c} \) (D-III).
