Concept:Work done by a constant force is the dot product of the force vector and the displacement vector.
Formula:$$ W = \vec{F} \cdot \vec{d} $$
Solution:- First, calculate the displacement vector \( \vec{d} \) by subtracting the initial position from the final position.
- \( \vec{d} = (6 - 2)\hat{i} + (5 - 3)\hat{j} = 4\hat{i} + 2\hat{j} \)
- Now, take the dot product of \( \vec{F} \) and \( \vec{d} \).
- \( W = (2\hat{i} + \hat{j}) \cdot (4\hat{i} + 2\hat{j}) \)
- \( W = (2 \times 4) + (1 \times 2) = 8 + 2 = 10 \text{ J} \)
Why other options are incorrect:Subtracting the coordinates incorrectly or failing to apply the dot product rule (e.g., multiplying mismatched components) leads to incorrect negative or larger values like -10, -18, or +18.
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