We know that we have 7 fundamental quantities (all scalars) and length is one of them. I classify velocity as a derived quantity. What about a position displacement vector? How do I classify displacement vector. Is it fundamental or derived quantity?
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It depends on the convention what to use as a fundamental quantity, but if you refer to SI it is:
- a derived quantity, if you refer to the electric displacement field,
$$ [D] = [\epsilon_0]\cdot [E] = [\epsilon_0]\cdot [F]/[Q] = \mathrm{\frac{A^2\, s^4}{kg\, m^3}\cdot \frac{kg\, m}{s^2}\cdot \left(A\, s\right)^{-1} = \frac{A\, s}{m^2}}. $$
- a fundamental quantity if you refer to a position displacement, because it is a length,
$$ [r] = \mathrm m. $$
