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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीConsider the following statements regarding the vector product (cross product) of two vectors \( \mathbf{a} \) and \( \mathbf{b} \): (A) \( \mathbf{a} \times \mathbf{b} = -\mathbf{b} \times \mathbf{a} \) (B) \( \mathbf{a} \times (\mathbf{b} + \mathbf{c}) = \mathbf{a} \times \mathbf{b} + \mathbf{a} \times \mathbf{c} \) (C) \( \mathbf{a} \times \mathbf{a} = 0 \) (D) Under coordinate reflection, \( \mathbf{a} \times \mathbf{b} \) reverses its direction. Which of the above statements are correct?
Correct answer · Option 1
(A), (B) and (C) only
Explanation
(A), (B), and (C) are standard true properties of vector products. (D) is incorrect because under coordinate reflection (parity inversion), \( (-\mathbf{a}) \times (-\mathbf{b}) = \mathbf{a} \times \mathbf{b} \), so the cross product (an axial vector) does not reverse its direction.
