Book Recommendations for vector algebra & calculus with proofs and concepts

Question

I am looking for a good book on vector algebra and vector calculus which just not states down formulas only but derives them ,gives logical justification and intuition. I have seen some related questions but they focus on either multivariable or more advanced calculus and doesn't answer my questions. I am a physics honours student( equivalent to major in foreign countries) . I am presently using Spiegel and Cambridge guide to vectors and tensor but both don't contain adequate theory (Spiegel is a problem book) for conceptual depth. Though i am physics student but also want to learn mathematics with the same conceptual clarity. I have seen Stewart,Thomas and Marsden/tromba calculus and they didn't address my queries. They introduce just the name and formulas with colourful pages except Marsden which has a little bit history; the rest contentall are same. For example in case of gradient they don't take pain to prove most property neither tell what is the meaning of such an operator why it's such so on . And other books that i have seen as suggestions on this forums other answers like Hubbard,Apostol, Spivak, Tarapov are way beyond my level and don't address vectors basics and directly move to higher tensor. I have just started 1st semester I know there are many mathematical physics books for us but i want to learn conceptually but those books teach it like formula tools. I want books which introduces vectors describe what are vector product(proof of dot and cross product formula), other operation, gradient, divergence,curl, green gauss theorem. It will be helpful if the book gives proof , justification of every thing with some analogies and generalisation and not too complex language. Any help would be appreciated. I don't want any book focusing mainly on multivariable calculus but more on vector.