A force F¯=(5i^−3j^+2k^)N moves a particle from r¯1=(2i^+7j^+4k^)m n to r¯2=(5i^+2j^+8k^)m . The work done by the force is,

S→=r→2−r→1 =3i^−5j^+4k^ W=F→.S→ =(5i^−3j^+2k^)(3i^−5j^+4k^) =15+15+8=38 J

A force F¯=(5i^−3j^+2k^)N moves a particle from r¯1=(2i^+7j^+4k^)m n to r¯2=(5i^+2j^+8k^)m . The work done by the force is,

S→=r→2−r→1 =3i^−5j^+4k^ W=F→.S→ =(5i^−3j^+2k^)(3i^−5j^+4k^) =15+15+8=38 J

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A force $\bar{F} = (5 \hat{i} - 3 \hat{j} + 2 \hat{k}) N$ moves a particle from ${\bar{r}}_{1} = (2 \hat{i} + 7 \hat{j} + 4 \hat{k}) m n to {\bar{r}}_{2} = (5 \hat{i} + 2 \hat{j} + 8 \hat{k}) m$ . The work done by the force is,

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18J

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38J

48J

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Detailed Solution

\vec{S} = {\vec{r}}_{2} - {\vec{r}}_{1}

$= 3 \hat{i} - 5 \hat{j} + 4 \hat{k}$

$W = \vec{F} . \vec{S}$

$= (5 \hat{i} - 3 \hat{j} + 2 \hat{k}) (3 \hat{i} - 5 \hat{j} + 4 \hat{k})$

$= 15 + 15 + 8 = 38 J$

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A force F¯=(5i^−3j^+2k^)N moves a particle from r¯1=(2i^+7j^+4k^)m n to r¯2=(5i^+2j^+8k^)m . The work done by the force is,

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A force $\bar{F} = (5 \hat{i} - 3 \hat{j} + 2 \hat{k}) N$ moves a particle from ${\bar{r}}_{1} = (2 \hat{i} + 7 \hat{j} + 4 \hat{k}) m n to {\bar{r}}_{2} = (5 \hat{i} + 2 \hat{j} + 8 \hat{k}) m$ . The work done by the force is,