Question

find the work done by force f=2i+3j+5k when it displaces a particle from r1=2i-3j+5k to r2=3i-4j+3k​

Answer 1

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Answer 2

To find:

Work done by force f=2i+3j+5k when it displaces a particle from r1=2i-3j+5k to r2=3i-4j+3k

Calculation:

First of all, let's find out the net displacement vector:

$\therefore \: \vec{r} = \vec{r2} - \vec{r1}$

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

$\implies \: \vec{r} = \hat{i} - \hat{j} - 2 \hat{k}$

Now, work done can be calculated from the dot product between force vector and displacement vector:

$\therefore \: W = \vec{F} \: . \: \vec{r}$

$\implies \: W = (2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \: . \: ( \hat{i} - \hat{j} - 2 \hat{k})$

$\implies \: W = 2 - 3 - 10$

$\implies \: W = - 11$

$\implies \: | W| = 11 \: joule$

So, work done is 11 joules.