Flashcards on Cross product
Cross Product Explained: Definition, Calculation & Applications
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Vector Cross Product
14 cards
Card 1
Question: What is the cross product?
Answer: The vector cross product is a binary operation performed on two vectors in three-dimensional Euclidean space that results in a new vector.
Card 2
Question: What kind of quantity does the cross product yield?
Answer: The cross product of two vectors results in a new vector.
Card 3
Question: How does the resultant vector of a cross product relate to the original vectors?
Answer: The resultant vector of a cross product is perpendicular to both of the original vectors.
Card 4
Question: What is the formula for the magnitude of the cross product of two vectors a and b?
Answer: |a × b| = |a||b|sin φ, where φ is the angle between vectors a and b.
Card 5
Question: What is the geometric interpretation of the magnitude of the cross product?
Answer: The magnitude of the cross product is equal to the area of the parallelogram formed by vectors a and b when they are placed tail-to-tail.
Card 6
Question: When is the magnitude of the cross product equal to 0?
Answer: If the vectors are parallel or anti-parallel (i.e., φ = 0 or φ = π), then |a × b| = 0.
Card 7
Question: What is the result of the cross product if the vectors are parallel or anti-parallel?
Answer: The cross product is the zero vector (0, 0, 0).
Card 8
Question: How is the direction of the cross product vector a × b determined?
Answer: The direction of the vector a × b is determined by the requirement that it must be perpendicular to the plane containing both vector a and vector b, a
Card 9
Question: Describe the right-hand rule for finding the direction of a × b.
Answer: Position your right hand so fingers point in the direction of a, curl fingers towards b, and your extended thumb will point in the direction of a × b.
Card 10
Question: Does the order of vectors matter in a cross product?
Answer: Yes, the order of the vectors in a cross product matters. a × b = -(b × a).