How to Understand Euclidean Geometry

3.2: Vectors

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all n -tuples of real numbers that have the form (x, x, …, x) with the standard operations on R^n | Numerade

You are familiar with the operations of gradient (∇ϕ), divergence (∇·V) and curl (∇×V) in ordinary vector analysis ia three-dimensional Euclidean space, Using covariant derivatives, derive formulae for these operations in spherical polar coordinates (r, 6, ϕ) defined by x=r sinθcosϕ y=r sinθsinϕ z=r cosθ Conpare your results to those in Jackson (1999) or an equivalent text. Are they identical? Should they be? | Numerade