find the work done in moving an object along a vector r=3i+2j-5k if the applied force is F=2i-j-k
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:
\(W=9\)
Step-by-step 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
\(W=3.2+2.(-1)+(-5).(-1)\)
\(W=6-2+5\)
\(W=9\)