Question

A particle is acted upon by constant forces
`vec(F)_(1)=(2hat(i)-3hat(j)+4hat(k))` and `vec(F)_(2)=(-hat(i)+2hat(j)-3hat(k))` is displaced from the point `A(2,1,0)` to the point `B(-3,-4,2)`. Find the total work done by the forces.

Answer 1

Here, `vec(F)_(1)=(2hat(i)-3hat(j)+4hat(k)) ,`
`vec(F)_(2)=(-hat(i)+2hat(j)-3hat(k))`
`vecr_(1)=(2hat(i)+hat(j)), vecr_(2)=(-3hat(i)-4hat(j)+2hat(k))`
Total force, `vecF=(vecF_(1)+vecF_(2))=(hat(i)-hat(j)+hat(k))`
displacement,
`vecr=(vecr_(2)-vecr_(1))=(-3hat(i)-4hat(j)+2hat(k))-(2hat(i)+hat(j))`
`=(-5hat(i)-5hat(j) +2hat(k))`
work done, `vecF.vecr=(hat(i)-hat(j)+hat(k))*(-5hat(i)-5hat(j)+2hat(k))`
`=-5+5+2=2units`