Objectives
After completing this chapter, you should be able to:
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Understand the cross product as an operation that produces a vector perpendicular to two given vectors, with its direction fixed by the right-hand rule.
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Interpret the magnitude of the cross product as the area of the parallelogram spanned by the two vectors, and recognize that the cross product is zero exactly when the vectors are parallel.
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Understand why the geometric and component definitions of the cross product describe one and the same object.
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Contrast the cross product with the dot product: one returns a vector and detects parallelism, while the other returns a scalar and detects perpendicularity.
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Understand torque as a measure of the turning effect of a force, and appreciate the role of cross product in determining torque.
