Vector concept?

Vector concept?

The definition of vector quantity and scalar quantity is simple: "the definition of vector and scalar quantity is as follows: (I will study it in detail in College Physics) (1) definition or explanation: some physical quantities should have numerical size (including relevant units) , it needs direction to be completely determined. The operations between these quantities do not follow the general algebraic rules, but follow the special algorithms. Such quantities are called physical vectors. Some physical quantities only have numerical size (including relevant units) and do not have directionality. The operations between these quantities follow the general algebraic rules. Such quantities are called physical scalars. (2) Note: ① the operation between vectors should follow special rules. The parallelogram rule is generally used for vector addition. The parallelogram rule can be extended to triangle rule, polygon rule or orthogonal decomposition method. Vector subtraction is the inverse operation of vector addition. Subtracting one vector from another is equal to adding the negative vector of that vector. A-B = a + (- b) . vector multiplication. The product of vector and scalar is still vector. The product of vector and vector can form a new scalar, and the product between vectors is called scalar product; it can also form a new vector, and the product between vectors is called vector product. For example, in physics, the scalar product of two vectors is used for the calculation of work and power. W = f · s, P = f · V, and in physics, two are used for the calculation of torque and Lorentz force Vector product of vector. M = R × F,F=qv × B. ② the vector expression of physical laws has nothing to do with the selection of coordinates. Vector symbols provide a simple and clear form for the expression of physical laws and simplify the derivation of these laws. Therefore, vectors are a useful tool for learning physics. "(3) there are two kinds of vectors. One is a physical quantity with only size and direction, such as velocity, which we call" odd vector "; Another kind of physical quantity not only has size and direction, but also a quantity of time required for the interaction between vectors to produce effect, such as force, which we call "even vector" or "limit (immediate, upper bound) vector", because the time required for their interaction between vectors to produce effect is immediate and the speed of light
In the computer, the vector graph can be enlarged infinitely and never deformed
Vector image
Vector image, also known as object-oriented image or drawing image, is mathematically defined as a series of vectors
The points connected by lines are listed. The graphic elements in the vector file are called objects. Each object is a self-contained entity with attributes such as color, shape, outline, size and screen position. Since each object is a self-contained entity, its attributes can be moved and changed many times while maintaining its original clarity and curvature, These features make vector based programs particularly suitable for legends and 3D modeling because they usually require the ability to create and manipulate a single object. Vector based drawing is independent of resolution. This means that they can be displayed on the output device at the highest resolution

Resultant force is the vector sum of the product of acceleration and mass of each part of the whole,

The product of acceleration and mass is force
F=ma
in other words
The resultant force is the vector sum of the forces of each part of the whole

The difference between the quantity product of a vector and the vector product of a vector

The quantity product of a vector is the product of numbers, and the result is quantity
The vector product of a vector is the sum of vectors on the right-hand rule component

Who can tell me the difference between vector product and vector product?

The order of magnitude is also called scalar product, and its operation result is scalar
The algorithm is a = b * C = b * c * cos&
Uppercase letters represent vectors (vectors), lowercase letters represent the friction of corresponding vectors, & represent the angle between two vectors. "*" is a multiplier sign, which is applied when writing,
Therefore, the operation of quantity product is often called "dot multiplication" in spoken language
Vector product is also called vector product, and its operation result is vector
The algorithm is a = B × C=b * c *Sin&
The direction is the right hand spiral, that is, the right hand clenches the fist, the thumb extends upward, and the four fingers vertically pass through the first vector and the second vector in the equation in turn. The thumb direction is the direction of vector a (note, b) × C and C × The result of B is different because the vector direction is different. And the results of B * C and c * B are the same)“ ×” It is a multiplication sign, which is used in writing, so the operation of vector product in spoken language is often called "cross multiplication"
Vector operation is widely used in physics, such as calculating the work of force w = f * s;
Linear velocity of circular motion v = w × R. Lorentz force F = Q * V × B et al

Quantity product of vectors The quantitative product of two vectors, for example, a · B = |a|b|cos θ The product of two vectors becomes the product of two real numbers | a | B | and becomes a real number after multiplication. Why can't it be expressed as a vector in the a direction or B direction after multiplication?

This is the definition of quantity product
a·b=|a||b|cos θ
If you want to represent the direction of a vector (such as a)
It can be expressed as a · B · A / | a| = | a| b| cos θ · a/|a|=|b|cos θ · a
Are you satisfied with this answer?

What is the formula of plane vector quantity product?

Let the vectors be x and Y respectively, and the product (which is a real number) be n
n=xycos α
among α Is the angle between two vectors when the starting point of two vectors is translated to a point