Shown are a position vector , [math]\vec{r}[/math] , a force vector , [math]\vec{F}[/math] , and the resulting moment vector , [math]\vec{M_O}[/math] . Moving the red dot will change the force and the blue dot changes the position.

After familiarization with the controls. Note: For a selected point the crossed arrows indicate you can move the point parallel to the xy plane and the opposing arrows indicate you can move the point parallel to the z-axis. [br][list][*]Check Projection[br][/*][/list]This will show the projection of the force to the direction of the position vector, [math]\vec{F_r}[/math] , and another component of the force perpendicular to [math]\vec{r}[/math]. Note that [math]\frac{\vec{r}\cdot\vec{F}}{\left|r\right|}[/math] is the magnitude of the projected vector and [math]\frac{\vec{r}}{\left|r\right|}[/math] is the unit direction vector of [math]\vec{r}[/math] and the vector dot product is also shown. Looking at the result how would the moment of [math]\vec{F_p}[/math] differ from the moment [math]\vec{r}\times\vec{F}[/math] and what would be the result of [math]\vec{r}\times\vec{F_r}[/math] .[br][list][*]Check Line Of Action[br][/*][/list]This will allow you to move the force vector along its line of action using slide. [math]_{\vec{r'}_1}[/math] is the new position vector which is shown at the top as r. An angle between the position and force vectors is also shown along with the length of the r[sub]1[/sub] vector. At what angle is the length of r[sub]1[/sub] a minimum?[br][list][*]Check Moment about an Axis[br][/*][/list]This will show an axis line that can be moved with the points O and L. [math]M_{OL}[/math] is the moment of the force about the axis OL. The moment arm (position vector) [math]\vec{r_2}[/math] is from a point on the axis to the application point of the force. This point can be moved with the slider. How does [math]M_{OL}[/math] vary with the position of the point? Also shown is the length of the moment arm and an angle between the axis and the moment arm. At what angle is the moment arm length minimum?