Question

A particle moves from position `3hat(i)+2hat(j)-6hat(k)` to `14hat(i)+13hat(j)+9hat(k)` due to a uniform force of `4hat(i)+hat(j)+3hat(k)N`. If the displacement is in meters, then find the work done by the force.

Answer 1

Here, `vecr_(1)=(3hat(i)+2hat(j)-6hat(k))m`
`vecr_(2)=(14hat(i)+13hat(j)-9hat(k))m`
`vecF=(4hat(i)+hat(j)-3hat(k))N`
`vec(s)=(vec(r_(2))-vec(r_(1)))`
`=(14hat(i)+13hat(j)+9hat(k))-(3hat(i)+2hat(j)-6hat(k))`
`=(11hat(i)+11hat(j)+15hat(k))m`
`W=vec(F).vecs=(4hat(i)+hat(j)-3hat(k))*(11hat(i)+11hat(j)+15hat(k))`
`=44+11-45=10J`