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 coordinates. Under a coordinate transformation, its components change inversely to the Jacobian matrix. Think of it as representing a physical vector like a displacement.
Contravariant Vector	A vector that transforms in the opposite way as the coordinates. Under a coordinate transformation, its components change by the Jacobian matrix. Think of it as representing a dual vector like a gradient.
Tensor	A multi-dimensional array of numbers whose components transform according to specific rules under a change of coordinates. Covariant and contravariant vectors are rank-1 tensors. Higher-rank tensors have multiple indices, some covariant and some contravariant.