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Teams A and B are playing a game of tug of war. The forces in which they pull at the rope are represented by vectors vec(a) and vec(b), respectively. Which option best describes the meaning of the following statement? || vec(a)||=2|| vec(b)|| Choose 1 answer: A Team A has twice as many people as team B. (B) Team A pulls twice as strongly as team B. (C) Team A is twice as far from the center of the rope as team B.

Teams A \mathrm{A} and B \mathrm{B} are playing a game of tug of war. The forces in which they pull at the rope are represented by vectors a⃗ \vec{a} and b⃗ \vec{b} , respectively.\newlineWhich option best describes the meaning of the following statement?\newline∥a⃗∥=2∣∣b⃗∣∣ \|\vec{a}\|=2|| \vec{b}|| \newlineChoose 11 answer:\newline(A) Team A has twice as many people as team B B .\newline(B) Team A pulls twice as strongly as team B.\newline(C) Team A is twice as far from the center of the rope as team B.

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Full solution

Q. Teams A \mathrm{A} and B \mathrm{B} are playing a game of tug of war. The forces in which they pull at the rope are represented by vectors a⃗ \vec{a} and b⃗ \vec{b} , respectively.\newlineWhich option best describes the meaning of the following statement?\newline∥a⃗∥=2∣∣b⃗∣∣ \|\vec{a}\|=2|| \vec{b}|| \newlineChoose 11 answer:\newline(A) Team A has twice as many people as team B B .\newline(B) Team A pulls twice as strongly as team B.\newline(C) Team A is twice as far from the center of the rope as team B.
  1. Magnitude Comparison: The statement ∣∣a⃗∣∣=2∣∣b⃗∣∣|| \vec{a}||=2|| \vec{b}|| is a vector magnitude comparison. It compares the magnitude (or length) of vector a⃗\vec{a} to the magnitude of vector b⃗\vec{b}. The double bars on each side of the vectors denote the magnitude (or norm) of the vectors, which represents the strength of the force in this context.
  2. Equation Meaning: The equation ∣∣a⃗∣∣=2∣∣b⃗∣∣|| \vec{a}||=2|| \vec{b}|| means that the magnitude of the force with which Team A pulls is twice the magnitude of the force with which Team B pulls. This is a direct comparison of the strengths of the forces, not the number of people on each team or their positions relative to the center of the rope.
  3. Correct Interpretation: Given the context of the problem, which is about the forces in a game of tug of war, the correct interpretation of the statement is that Team A pulls twice as strongly as team B. This corresponds to option (B)(B) from the given choices.

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