The shortest path combination problem is a classical mathematical problem, which mainly refers to the arrangement and combination of high schools. It is mostly based on the number axis and coordinate system and can be modified by streets and hutongs. Originated from the problem of "electronic ants" in various exercises.

Travel distance

A particle moves from one position to another in space, and the length of the trajectory is called the distance traveled by the particle in this movement. Distance is a scalar, that is, a quantity without direction.

Displacement and distance are two different physical quantities. In linear motion, the distance is the length of the linear trajectory; In curved motion, the distance is the length of the curve trajectory. When an object returns to its original place after a period of movement, the distance is not zero and the displacement is equal to zero.

quantity

Scalar, also called "no vector". Some physical quantities have only numerical values, no direction, and some are positive and negative. In physics, scalar or scalar refers to a physical quantity that remains unchanged under coordinate transformation. Generally speaking, scalar is a quantity with only size and no direction.

definition

Scalar, also known as "no vector". Some physical quantities have only numerical values, no direction, and some are positive and negative. The operation between these quantities follows the general algebraic law and is called "scalar".

Such as mass, density, temperature, work, energy, distance, speed, volume, time, heat, resistance, power, potential energy, gravitational potential energy, electric potential energy and other physical quantities. No matter what coordinate system you choose, the scalar value remains the same. 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 scalars is called scalar product. The product of vectors is called cross product. Such as work and power, are calculated by using the scalar product of two vectors. W=F S, p = f v. Calculation of torque, Lorentz force, etc. Take the vector product of two vectors. M=r×F，F=qvB .

In physics, scalar or scalar refers to a physical quantity that remains unchanged under coordinate transformation. For example, the distance between two points in Euclidean space is unchanged under coordinate transformation, and the space-time interval in relativistic four-dimensional space-time is unchanged under coordinate transformation. In this way, the components of the relative vector have different values in different coordinate systems, such as velocity.

Generally speaking, scalar is a quantity with only size and no direction. In contrast, vectors have both size and direction.