Engineering Statics

B-22


Find the moment about line L = 3i + j -2k of the vector F = 10i + 20j + 5k at a position defined by r = 3i - 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 is defined as the triple vector product of the 
unit vector about the line, the position vector and the force vector placed 
in rows one, two and three respectively.  Note that since no vectors appear 
in the determinant the answer will be a scalar.
Evaluating the determinant gives the moment about a line as a scalar.  If 
the answer is positive the moment about the line is in the same sense as 
the unit vector.  A negative moment indicates that it is in the opposite 
direction.