Flashcards on Vector addition and subtraction
Vector Addition and Subtraction: A Comprehensive Guide for Students
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Vector Operations
33 cards
Card 1
Question: How do you find the sum of two vectors A = (Aₓ, Aᵧ) and B = (Bₓ, Bᵧ)?
Answer: The resultant vector R is given by R = (Aₓ + Bₓ, Aᵧ + Bᵧ).
Card 2
Question: How is vector addition extended to three dimensions?
Answer: R = (Aₓ + Bₓ, Aᵧ + Bᵧ, A₂ + B₂).
Card 3
Question: Once the components of a resultant vector R are known (Rₓ, Rᵧ), how is its magnitude calculated?
Answer: |R| = √(Rₓ² + Rᵧ²).
Card 4
Question: How is the direction (angle θ with the positive x-axis) of a resultant vector R found?
Answer: θ = arctan(Rᵧ / Rₓ), paying attention to the quadrant of the resultant vector.
Card 5
Question: What is the commutative property of vector addition?
Answer: The order in which vectors are added does not affect the resultant: A + B = B + A.
Card 6
Question: What is the associative property of vector addition?
Answer: When adding three or more vectors, the grouping of vectors does not affect the resultant: (A + B) + C = A + (B + C).
Card 7
Question: If vector A = (3.0 m, 4.0 m) and vector B = (2.0 m, -6.0 m), what is the resultant vector R?
Answer: R = (5.0 m, -2.0 m).
Card 8
Question: For the resultant vector R = (5.0 m, -2.0 m), what is its magnitude?
Answer: |R| ≈ 5.39 m.
Card 9
Question: For the resultant vector R = (5.0 m, -2.0 m), what is its direction?
Answer: θ ≈ -21.8° (or 338.2° from the positive x-axis, measured counter-clockwise).
Card 10
Question: How can vector subtraction (A - B) be understood in terms of vector addition?
Answer: It is equivalent to adding vector A to the negative of vector B (A + (-B)).