The non-commutative property of a vector product is
Correct answer: D. A x B = -B x A
- A. A . B = B . A
- B. A x B = B x A
- C. A . B = -B . A
- D. A x B = -B x A
Explanation
The correct answer is A x B = -B x A. This reflects the non-commutative property of the vector product, meaning that reversing the order of the vectors changes the sign of the result. Option A is incorrect as it describes the commutative property of the scalar product, not the vector product. Option B incorrectly states that the vector product is commutative, which it is not. Option C incorrectly suggests that the scalar product is anti-commutative, but it is actually commutative.
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About Vector Product
The vector product, or cross product, gives a vector perpendicular to two multiplying vectors, with magnitude AB sin θ and direction set by the right-hand rule. It covers properties such as anti-commutation, area from cross products, torque and angular momentum. Unlike the dot product, its result is a vector.
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