Question

Find the work done in moving an object along a vector r=3i+2j-5k if the applied force is F=2i-j-k

Answer 1

The work is equivalent to the dot product of the two vectors.


`W=\mathbf F\cdot\mathbf r=\langle2,-1,-1\rangle\cdot\langle3,2,-5\rangle=6-2+5=9`

Answer 2

`W=9`

Explanation:

applying the following formula

`W=r.f`

here the dot indicates the dot product

then

`W=(3i+2j-5k).(2i-j-k)`

taking dot product

`W=3.2+2.(-1)+(-5).(-1)`

`W=6-2+5`

`W=9`