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}Â 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.

#### Solution:

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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

\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

5=-1+6z

-14=-2-6y

Solving the equations gives us:

y=2 m

z=1 m

z=1 m

#### Final Answers:

y=2 m

z=1 m

z=1 m