A force F→=5i−3j+2k moves a particle from r→1=2i+7j+4k to r→2=5i+2j+8k . Calculate the work done.

r¯1+s¯=r2 s=r¯2−r¯1 r¯1=2i^+2j^+4k^ r¯2=5i^+2j^+8k^ F=5i^−3j^+2k^ S=3i^−5j^+4k^ ω=F¯.S¯ =15+15+8 =38 units

A force F→=5i−3j+2k moves a particle from r→1=2i+7j+4k to r→2=5i+2j+8k . Calculate the work done.

r¯1+s¯=r2 s=r¯2−r¯1 r¯1=2i^+2j^+4k^ r¯2=5i^+2j^+8k^ F=5i^−3j^+2k^ S=3i^−5j^+4k^ ω=F¯.S¯ =15+15+8 =38 units

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A force $\vec{F} = 5 i - 3 j + 2 k$ moves a particle from ${\vec{r}}_{1} = 2 i + 7 j + 4 k t o {\vec{r}}_{2} = 5 i + 2 j + 8 k$ . Calculate the work done.

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30 units

15 units

38 units

20 units

answer is A.

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Detailed Solution

{\bar{r}}_{1} + \bar{s} = r_{2}

$s = {\bar{r}}_{2} - {\bar{r}}_{1}$

${\bar{r}}_{1} = 2 \hat{i} + 2 \hat{j} + 4 \hat{k}$

${\bar{r}}_{2} = 5 \hat{i} + 2 \hat{j} + 8 \hat{k}$

$F = 5 \hat{i} - 3 \hat{j} + 2 \hat{k}$

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

$ω = \bar{F} . \bar{S}$

$= 15 + 15 + 8$

$= 38 units$

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A force F→=5i−3j+2k moves a particle from r→1=2i+7j+4k to r→2=5i+2j+8k . Calculate the work done.

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A force $\vec{F} = 5 i - 3 j + 2 k$ moves a particle from ${\vec{r}}_{1} = 2 i + 7 j + 4 k t o {\vec{r}}_{2} = 5 i + 2 j + 8 k$ . Calculate the work done.