Scalar, also known as "vector free". Some physical quantities have only numerical value, but no direction. Some of them are positive or negative. The operation between these quantities follows the general Algebra The rule is called "scalar". Such as mass, density, temperature Work , energy distance 、 rate , volume, time, heat resistance , power potential energy 、 gravitation Potential energy potential Can equal physical quantity. Whatever you choose Coordinate system The scalar value remains unchanged. The product of a vector and a scalar is still a vector. The product of scalar and scalar is still scalar. The product of vector and vector can form a new scalar or a new vector. The product of scalar is called Scalar product ； The product of vectors is called vector product. For example, the calculation of work and power is based on the scalar product of two vectors. W=F·S，P=F·v。 moment 、 Lorentz force The vector product of two vectors is used for the calculation of, etc. M=r×F，F=qvB。 In physics, scalar (or pure quantity) coordinate transformation Lower invariant physical quantity 。 For example, Euclidean space The distance between the middle two points remains unchanged under coordinate transformation, relativity Four-dimensional space-time in Spatiotemporal interval It remains unchanged under coordinate transformation. This relative vector weight In different Coordinate system There are different values in, such as speed. In popular terms, a scalar is a quantity with only size and no direction. (In contrast, a vector has both size and direction.) 
Physical vector diagram Some scalars use positive and negative to express the size, such as Gravitational potential energy 、 potential Some scalars use positive and negative to express properties, such as the amount of charge, positive charge means that the object is positively charged, and negative charge means that the object is negatively charged. Some scalars use positive and negative to express trends, such as work, and the positive and negative of work represent energy conversion The tendency of force to do Positive work , object's kinetic energy Increase Negative work , the kinetic energy of the object decreases (decreasing trend). Scalar positive and negative only represent size, independent of direction. Note: Scalar does not comply Parallelogram rule ！ Definition of vector and scalar:
(Will study in detail in college physics)
(1) Definition or explanation: some physical quantities must have numerical value (including relevant units) and be completely determined by direction. The operation between these quantities does not follow the general algebraic rules, but follows the special operation rules. Such quantities are called physical vectors. Some physical quantities only have numerical values (including relevant units), but do not have directionality. The operations between these quantities follow general algebraic rules. Such quantities are called physical scalars.
(2) Note: ① The operation between vectors should follow special rules. Vector addition is generally available Parallelogram rule 。 The parallelogram rule can be extended to Triangle rule , polygon rule or Orthogonal decomposition method Etc. vector subtraction Is vector additive Inverse operation Subtracting one vector from another is equal to adding the negative vector of that vector. A-B=A+(-B)。 Vectorial multiplication 。 The product of a vector and a scalar is still a vector. The product of vectors and vectors can form new scalars. The product between vectors is called Scalar product ； It can also form new vectors. The product between vectors is called vector product. This is similar to the vector Knowledge is consistent. For example, in physics, the calculation of work, power, etc. uses the scalar product of two vectors. W=F·S，P=F·v， In physics, the calculation of torque and Lorentz force is the vector product of two vectors. M=r×F，F=qv×B。② The vector expression of physical laws has nothing to do with the choice of coordinates. Vector symbols provide a simple and clear form for expressing physical laws, and simplify the derivation of these laws. Therefore, vectors are useful tools for learning physics. 
