A force $\to F = 3 ˆ i + 4 ˆ j + ˆ k$ displaces a body from a point with coordinates $(1, 2, 1)$ to another points with coordinates $(2, 0, 3)$ . Calculate the work done by the force. All physical quantities are in $S I$ units :

(+3)J

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(-6)J

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(-3)J

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(+6)J

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Solution

The correct option is C (-3)J
$\to F = 3 ˆ i + 4 ˆ j + ˆ k$

As, $W . D = \int \to F . \to d x \to F = 3 ˆ i + 4 ˆ j + ˆ k \to d x =_{f} -_{i} = 1 ˆ i - 2 ˆ j + 2 ˆ k ∴ W . D = (ˆ 3 i + 4 ˆ j + ˆ k) . (1 ˆ i - 2 ˆ j + 2 ˆ k) = 3 - 8 + 2 W = - 3 J$

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