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  4. If under the action of a force (4i+j+3k)N, a particle moves from position r1=3i+2j-6k to position r2=14i+13j+9k, then the work done will be

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Q. If under the action of a force $ (4i+j+3k)N, $ a particle moves from position $ {{r}_{1}}=3i+2j-6k $ to position $ {{r}_{2}}=14i+13j+9k, $ then the work done will be

Bihar CECEBihar CECE 2012

Solution:

Here, $r _{1}=3 i +2 j -6 k$
and $r _{ 2 }=14 i +13 j +9 k$
So, displacement, $\left( r _{ 2 }- r _{ 1 }\right)=$
$(14 i +13 j +9 k )-(3 i +2 j -6 k )$
$=11 i +11 j +15 k$
Hence, work done
$= F \cdot s$
$=(4 i + j +3 k ) \cdot(11 i +11 j +15 k )$
$=44+11+45=100\, J$