Engineering Statics

B-23


Find the moment about line L = 4i+5j+3k of the vector F = 20i+60j+90k at a position defined by r = 40j.

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 and then finding the scalar product 
between the moment and the unit vector associated with the line.
The moment about the line is the scalar obtained when the dot product 
of the unit vector of the line is taken with the moment about any point 
on the line.
Substituting in for the unit vector and the force yields a scalar. 
Remember that the dot product of like unit vectors equals 1.
Performing the arithmetic yields the scalar for the moment about the line.