My professor insists that weight is a scalar. I sent him an email explaining why it's a vector, I even sent him a source from NASA clearly labeling weight as a vector. Every other source also identifies weight as a vector.
I said that weight is a force, with mass times the magnitude of gravitational acceleration as the scalar quantity and a downward direction.
His response, "Weight has no direction, i.e., it is a scalar!!!" My thought process is that since weight is a force, and since force is a vector, weight has to be a vector. This is the basic transitive property of equality.
Am I and all of these other sources wrong about weight being a vector? Is weight sometimes a vector and sometimes a scalar?
After reading thoroughly through his lecture notes, I discovered his reasoning behind his claim:
Similarly to how speed is the scalar quantity (or magnitude) of velocity, weight is the scalar quantity (or magnitude) of the gravitational force a celestial body exerts on mass.
I'm still inclined to think of weight as a vector for convenience and to separate it from everyday language. However, like one of the comments stated, "Definitions serve us."
Best Answer
On earth, weight of a body is defined as the force by which the body is attracted by the earth towards its center. Weight can thus be considered the same as the gravitational force exerted by the earth on that body. Hence, weight can be deemed a vector since it is a force, irrespective of the planet you consider. $$\vec W=m\vec g=\frac{GMm}{r^2}\hat r$$ As mentioned in the comments, since $g$ has the same direction (directed towards the center of the concerned planet) always, it might be(?) considered a scalar. Thats what your prof is doing. But strictly speaking, weight is a vector.
Hope this helps you.