Anticommutative property
from class:
College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
The anticommutative property states that the order of the operands affects the sign of the result. Specifically, for vectors, $\mathbf{a} \times \mathbf{b} = - (\mathbf{b} \times \mathbf{a})$.
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5 Must Know Facts For Your Next Test
- The anticommutative property is essential when dealing with the cross product of two vectors.
- It implies that swapping the vectors in a cross product changes the direction of the resulting vector to its opposite.
- The property is used to determine torque and angular momentum calculations in physics.
- Understanding this property helps in solving problems related to rotational dynamics and forces in three dimensions.
- It highlights that not all vector operations are commutative, contrasting with dot products which are commutative.
Review Questions
- What does the anticommutative property imply about the cross product of two vectors?
- How does changing the order of vectors in a cross product affect the result?
- Give an example where the anticommutative property is applied in physics.
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