What is the dot product of two vectors that are parallel?

1 Answer
Jan 15, 2015

It is simply the product of the modules of the two vectors (with positive or negative sign depending upon the relative orientation of the vectors).
A typical example of this situation is when you evaluate the WORK done by a force #vecF# during a displacement #vecs#.
For example, if you have:
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Work done by force #vecF#:
#W=|vecF|*|vecs|*cos(theta)#
Where #theta# is the angle between force and displacement; the two vectors being parallel can give:

#theta=0°# and #cos(theta)=cos(0°)=1# so:
#W=5*10*1=50 J#

Or:

#theta=180°# and #cos(theta)=cos(180°)=-1# so:
#W=5*10*-1=-50 J#