Question #25150

define scaler and vector quantities?

Expert's answer

A scalar quantity is a quantitythat is invariable with respect to any system of coordinates, i.e. it never

changes because of a transformation of coordinates. In comparison to vector

quantities, a scalar is remarkable because it has only a magnitude, but no

direction. A vector quantity is a quantity that is characterized both by a

magnitude and a direction, and its coordinates change, obeying certain rules,

if a transformation of coordinates takes place.

In a broader framework of tensors, a scalar is a tensor of 0-th order (and has

just 1 coordinate), whereas a vector is a tensor of 1-st order (and has 3

coordinates). The next would be a tensor of 2-nd order, which is essentially a

matrix 0f 3x3 with 9 values.

changes because of a transformation of coordinates. In comparison to vector

quantities, a scalar is remarkable because it has only a magnitude, but no

direction. A vector quantity is a quantity that is characterized both by a

magnitude and a direction, and its coordinates change, obeying certain rules,

if a transformation of coordinates takes place.

In a broader framework of tensors, a scalar is a tensor of 0-th order (and has

just 1 coordinate), whereas a vector is a tensor of 1-st order (and has 3

coordinates). The next would be a tensor of 2-nd order, which is essentially a

matrix 0f 3x3 with 9 values.

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