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I have just come onto working with vectors in pure mathematics and have no problems calculating with them. However, I do not really understand the difference between a vector and a scalar.

A scalar has magnitude only.

A vector has magnitude and direction.

Since trying to satisfy myself of the difference between these two objects, I have learned that scalars can be real numbers and are related to the operation of scaling a vector.

-7 is a scalar quantity althought it appears, to me at least, to be directed. I have been told that the negative is an indication of sense rather than direcition but this is a source of confusion for me. The magnitude of a scalar makes sense when I think of it as a vector. It seems to me as though it is a one-dimensional vector.

Would someone please clarify the difference between a scalar and a vector or provide any comments that could clear up this confusion?

Thank-you.