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I think it would be beneficial to physics learners in general if we
could clear up this confusion once and for all. Consider the following
scenario: A block has a bunch of forces, all lying in one plane, acting
on it, including a force exerted on the block by a rigid strut (of
negligible mass) which lies in the plane of the forces and is
pin-connected (frictionless pins perpendicular to the plane of the
forces) on one end to the block and on the other end to something else.
Other than the pins, nothing is exerting a force on the strut. The
orientation of the strut is specified in the problem statement. The
question is, what is the force exerted on the block (plus the pin on the
block, which is considered to be part of the block) by the strut?
Enough information about the other forces is provided to make the
problem solvable. Each student that solves the problem draws a free
body diagram using a point of view in which the strut extends up and to
the right at the specified angle above the horizontal.
Now it is time for the teacher to prepare a mini lecture for the entire
class. If you were the teacher, besides the obvious statement about the
magnitude of a vector being positive by definition, what would you say
to the students?
If you choose to designate the strut-force-related arrow as a basis
vector, how would you indicate on the diagram that it is a basis vector
rather than a physical vector?
Label it "basis vector"? (Does one then
also need to label each physical vector "physical vector"?)
Or would
you use two parallel lines ==== to depicted the shaft of a basis arrow
vector rather than the single line ---- that you use to depict the shaft
of a physical vector? Where would you put the "F_s"?