Questions: Consider two velocity vectors vA and vB which have the same magnitude s and different directions as shown in the figure. Which of the following correctly describes vA-vB ? (A) A vector with magnitude zero. B A vector with a magnitude greater than zero and less than s. (C) A vector with a magnitude equal to s. (D) A vector with a magnitude greater than s.

Consider two velocity vectors vA and vB which have the same magnitude s and different directions as shown in the figure. Which of the following correctly describes vA-vB ? (A) A vector with magnitude zero. B A vector with a magnitude greater than zero and less than s. (C) A vector with a magnitude equal to s. (D) A vector with a magnitude greater than s.
Transcript text: Consider two velocity vectors $\vec{v}_{\mathrm{A}}$ and $\vec{v}_{\mathrm{B}}$ which have the same magnitude $s$ and different directions as shown in the figure. Which of the following correctly describes $\left|\vec{v}_{\mathrm{A}}-\vec{v}_{\mathrm{B}}\right|$ ? (A) A vector with magnitude zero. B A vector with a magnitude greater than zero and less than $s$. (C) A vector with a magnitude equal to $s$. (D) A vector with a magnitude greater than $s$.
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Solution

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Solution Steps

Step 1: Identify the given vectors

The problem provides two velocity vectors, \(\vec{v}_A\) and \(\vec{v}_B\), which have the same magnitude but different directions.

Step 2: Determine the operation to be performed

The question asks for the result of the vector subtraction \(\vec{v}_A - \vec{v}_B\).

Step 3: Analyze the direction and magnitude

Since \(\vec{v}_A\) and \(\vec{v}_B\) have the same magnitude but different directions, the vector subtraction \(\vec{v}_A - \vec{v}_B\) will result in a vector that has a magnitude greater than zero and a direction that depends on the relative directions of \(\vec{v}_A\) and \(\vec{v}_B\).

Final Answer

A vector with a magnitude greater than zero.

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