# If the force acts at a point having

A force of $F=\left\{6i-2j+1k\right\}$ kN produces a moment of $M_o=\left\{4i+5j-14k\right\}\,\text{kN}\cdot\text{m}$ about the origin of coordinates, point O. If the force acts at a point having an x coordinate of x = 1 m, determine the y and z coordinates.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

The moment is found by taking the cross product between a position vector from the origin and the force. Thus, we can write:

$M_o=r\times F$

Substitute the values we know:

$\left\{4i+5j-14k\right\}=\begin{bmatrix}\bold i&\bold j&\bold k\\1&y&z\\6&-2&1\end{bmatrix}$

$\left\{4i+5j-14k\right\}=(y+2z)i-(1-6z)j+(-2-6y)k$

Separating the components gives us:

$4=y+2z$

$5=-1+6z$

$-14=-2-6y$

Solving the equations gives us:

$y=2$ m

$z=1$ m

$y=2$ m
$z=1$ m