Question

The momentum of the force F=4i+5j-6k at (3,1,5) about the point (3,3,4):is given by

Answer 1

The force is given as $F=4\hat i+5\hat j-6\hat k$

The force is acting at (3,1,5).

The point under consideration is ( 3,3,4).

The displacement vector between these points is $(3-3)\hat i+(1-3)\hat j+(5-4)\hat k$

Hence, the displacement  vector [ r ]  = $0\hat i-2\hat j+1\hat k$

We are asked to calculate the moment of the force.

The moment of the force is calculated as -

 $\vec \tau=\ \vec r\times \vec F$

  $=\ (4\hat i+5\hat j-6\hat k)\times (0\hat i-2\hat j+1\hat k)$    

                  $=\ [5\times 1-(-2)\times (-6)]\hat i+[0\times (-6)-4\times 1]\hat j+[4\times (-2)-0\times 5]\hat k$

                 $=-7\hat i-4\hat j-8\hat k$

Hence, the moment of the force is $-7\hat i-4\hat j-8\hat k$