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 vecFF during a displacement vecss.
For example, if you have:
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Work done by force vecFF:
W=|vecF|*|vecs|*cos(theta)W=Fscos(θ)
Where thetaθ 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