The cross-product of two vectors is a negative vector when:
Correct answer: D. They are rotated through 270°
- A. They are parallel vectors
- B. They are anti-parallel vectors
- C. They are perpendicular vectors
- D. They are rotated through 270°
Explanation
The cross-product of two vectors, A and B, is defined as a vector that is perpendicular to both A and B, with a magnitude given by |A||B|sin(θ), where θ is the angle between the vectors. The direction of the cross-product is determined by the right-hand rule. For parallel (0°) and anti-parallel (180°) vectors, the cross-product is zero because sin(0°) = sin(180°) = 0. For perpendicular vectors (90°), the cross-product is maximized and not inherently negative. However, when one vector is rotated 270° from the other, the cross-product points in the opposite direction of a 90° rotation according to the right-hand rule, which can be considered negative in terms of direction.
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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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