A constant force F=8i+0j−7k moves an object along a straight line from point (1, 4, 9) to point (-2, -6, -6). Find the work done if the distance is measured in meters and the magnitude of the force is measured in newtons.

Question

anonymous · Answer

Find the angle @ between the force and the displacement vector, then use
work= (force)(displacement) cos @

parthkohli · Answer

Hello!  This is once of the situations when the angle between two vectors is not needed.  The force vector has been given to you.  The displacement vector would just be the vector pointing from $(1,4,9)$ to $(-2,-6,-6)$ which would be $(-2 - 1)\hat i + (-6 - 4)\hat j + (-6 - 9)\hat k = -3\hat i - 10\hat j - 15 \hat k$.

Now, work is $\bf F \cdot s$

parthkohli · Answer

What is $(8\hat i - 7\hat k ) \cdot (-3 \hat i - 10 \hat j - 15 \hat k)$?

anonymous · Answer

Good point. Not clear whether vector dot product is familiar to student, though.

parthkohli · Answer

Probably it should!  These types of questions generally come in dot products.

anonymous · Answer

Certainly a cleaner way of solving the problem.