Define the terms: contravariant, covariant vectors and tensors.

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Term	Definition
Covariant Vector	A vector that transforms in the same way as the coordinate system. Think of it as a physical vector, like displacement. Its components change inversely to a coordinate transformation.
Contravariant Vector	A vector that transforms oppositely to the coordinate system. Think of it as a dual vector, like a gradient. Its components change directly with a coordinate transformation.
Tensor	A multi-dimensional array of numbers that transforms according to specific rules under coordinate transformations. Covariant and contravariant vectors are rank-1 tensors. Higher-rank tensors have multiple covariant and/or contravariant indices, indicating how they transform.