Engineering Statics

B-24


  Find the moment about line L = 6i-3j+2k of the vector F = i-4j+8k at a position defined by r = j-4k.

The force is given in vector form.
The position is given in vector form.
The line is given in vector form.
The unit vector is a vector in the direction of <B><I>L</I></B> is found by dividing 
the vector <B><I>L</I></B> with its magnitude.
The moment about a line can also be calculated by first finding the 
moment about any point on the line (given by <B><I>r</I></B>x<B><I>F</I></B>) 
and then finding the 
scalar product between the moment and the unit vector associated with 
the line.
The moment about a line can also be calculated by first finding the 
moment about any point on the line (given by <B><I>r</I></B>x<B><I>F</I></B>) 
and then finding the scalar product 
between the moment and the unit vector associated with the line.
Evaluating the determinant gives the value of <B><I>r</I></B>x<B><I>F</I></B> as a vector.
The moment about the line is the dot product of the unit vector along 
the line and the moment found in the previous step.
Substituting in for the unit vector and the moment vector yields the scalar expression for the moment about the line.