I am taking a course on GR and trying to understand Tensor calculus. I think I understand contravariant tensor (transformation of objects such as a vector from one frame to another) but I am having a hard time with covariant tensors. I looked into the Wikipedia page (https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors) and came across this figure: (https://upload.wikimedia.org/wikipedia/commons/b/b2/Basis.svg) https://upload.wikimedia.org/wikipedia/commons/b/b2/Basis.svg The contravariant part makes sense. Vector A is decomposed into components along e1 and e2. However, I do not understand what is meant by "The covariant components are obtained by projecting onto the normal lines to the coordinate hyperplanes." In which direction are these normal lines pointing. I'd appreciate if anyone can help me visualize what is happening.