Question

two forces F1= 2i + 3j -4k and F2=i+j-k acting on a particle causes it to shift from (1,2,3) to (2,4,5) the worj done by resultant force is​

Answer 1

Given :-

${F}_{1} = 2\hat{i} + 3\hat{j} - 4\hat{k}$

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

${S}_{1} = \hat{i} + 2\hat{j} + 3\hat{k}$

${S}_{2} = 2\hat{i} + 4\hat{j} + 5\hat{k}$

Now, The distance travelled.

S = ${S}_{2}-{S}_{1}$

$S\:= \hat{i} + 2\hat{j} + 2\hat{k}$

F = ${F}_{1}+{F}_{2}$

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

As we know that,

W = F•S

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

W = (3 + 8 - 10)J

W = (11 - 10)J

W = 1 J

Hence,

Option (1) is correct.