Subtraction of vectors. How is the addition and subtraction of vectors calculated?

Subtraction of vectors. The two vectors share a starting point, connect the end points, and point to the reduced vector.

1. Vector subtraction can be regarded as the inverse of vector addition. Vector addition is well mastered and easy to master: vectors are connected from end to end, and the vectors from the beginning of the first vector to the end of the last vector are their sum vectors.

The sum of a closed polygon vector consisting of multiple vectors end-to-end, the sum of which is zero. The sum of the two vectors is the easiest to grasp. Two vectors are connected end to end, and the vector from the start to the end is the sum of the two vectors.

2. Put the starting point of the two vectors into a common starting point, the vector that leads from the end point of one vector to the end of the other vector is the difference vector between the two, and the arrow points to whoever is the subtractive vector.

3. Vector subtraction operation in plane coordinate system:

Vector a=(x1,y1), vector(x2,y2, vector c=vector a-vector b,c=(x1-x2,y1-y2)

4. Vector subtraction operation in spatial coordinate system:

vector a = (x1, y1, z1, vector (x2, y2, z2, vector c = vector a - vector b, c = (x1-x2, y1-y2, z1-z2).

Extended information: The triangle rule solves the addition and subtraction of vectors: connect each vector one after the other, and the result is that the starting point of the first vector points to the end of the last vector.

The parallelogram rule solves the vector addition method: translate the two vectors to the common starting point, and use the two sides of the vector to make a parallelogram, and the result is the diagonal of the common starting point.

The parallelogram rule solves the vector subtraction method: translate the two vectors to a common starting point, and make a parallelogram with the two sides of the vector, and the result is from the end point of the reduced vector to the end point of the reduced vector.

The parallelogram rule only applies to the addition and subtraction of two non-zero non-collinear vectors. ）

Coordinate System Solution Vector Addition and Subtraction:

In a Cartesian coordinate system, the origin is defined as the starting point of the vector. The coordinates of the sum and difference of the two vectors are equal to the sum and difference of the corresponding coordinates of the two vectors, respectively, if the vector is expressed as (x,y) and a(x1,y1).

b(x2,y2), then a+b=(x1+x2,y1+y2),a-b=(x1-x2,y1-y2).

To put it simply: the addition and subtraction of a vector is the addition or subtraction of the corresponding component of the vector. Orthogonal decomposition similar to physics.

Subtraction. A vector equal in length and in the opposite direction is called the opposite vector of a, (a) a, the opposite vector of the zero vector is still a zero vector.

1）a＋(－a)＝(a)＋a＝0（2）a－b＝a＋(－b)。The end point of the subtractive vector is taken as the starting point, and the end point of the subtracted vector is emphasized.

All the formulas for the operation of vectors are:

1. Addition: If the vectors ab and bc are known, and then the vector ac is made as the vector ac, then the vector ac is called the sum of ab and bc, which is recorded as ab+bc, that is, ab+bc=ac.

2. Subtraction: ab-ac=cb, this calculation method is called the triangle rule of vector subtraction, which is abbreviated as: the common starting point, the middle point, and the subtraction.

3. Number multiplication: The product of the real number and the vector a is a vector, and this operation is called the number multiplication of the vector, which is denoted as a. When >0, a has the same direction as a, when <0, a has the opposite direction to a, and when =0, a=0.

Vector Algebra Rules:

1. Anticommutative law: a b=-b a.

2. The distributive property of addition: a (b+c)=a b+a c.

3. Compatible with scalar multiplication: (ra) b=a (rb)=r(a b).

4. The associative law is not satisfied, but the Jacobian identity is satisfied: a (b c) + b (c a) + c (a b) = 0.

The law of vector subtraction is the law of triangles.

Similarly, put the start points of the two vectors together and connect the two end points, which is the difference, and the direction of the difference vector points to the reduced vector.

If a and b are opposite vectors, then a=-b, b=-a, a+b=0The inverse of 0 is with 0, oa-ob=ba, i.e., "common starting point, pointing to the subtraction".

a=(x1,y1),b=(x2,y2), then a-b=(x1-x2,y1-y2).

Addition and subtraction transformation law: a+(-b)=a-b

is a-b = (x1-x2, y1-y2).

Subtraction of vectors: If a and b are opposite vectors, then the inverses of a=-b, b=-a, and a+b= are 0oa-ob=baThat is, the "common cautious starting point, pointing to the subtracted" side town, for example:

a=(x1,y1),b=(x2,y2), then a-b=(x1-x2,y1-y2).

Algebraic rules

1. Anticommutative law: a b=-b a.

2. The distributive property of addition: a (b+c)=a b+a c.

3. Compatible with scalar multiplication: (ra) b=a (rb)=r(a b).

4. It does not satisfy the associative law, but satisfies the coarse comparable identity of the Yayun ruler: a (b c) + b (c a) + c (a b) = 0.

5. The distributive property, linearity, and Jacobian identities show that R3 with vector addition and cross product constitutes a Lie algebra.

Vector subtraction is the inverse operation of vector addition, the starting point of two vectors is put into a common starting point, the vector leading from the end point of one vector to the end of another vector is the difference vector between the two, and the arrow points to whoever is the subducted vector. In mathematics, vectors are also known as Euclidean vectors, geometric vectors, vectors, and refer to quantities with magnitude and direction, which can be visualized as line segments with arrows, and the arrows point to represent the direction of the vector.

Understanding of vector subtractionVector subtraction is defined with the help of opposite vectors and vector addition, in fact, the essence of vector subtraction is the inverse operation of vector addition The difference between the two vectors is still a vector. When making a difference vector, method 1 is more complicated, method 2 is simpler, and it should be flexibly used according to the needs of the problem.

The subtraction of two vectors is to find their difference vector and destroy it, and the result is that the end point of the reduced vector is the starting point, and the end point of the reduced vector is the end vector Simply put, the end point of the reduced vector points to the end point of the reduced vector Naturally, Sen Nianbei can think that any vector can be expressed as the difference between any two vectors Again, according to the meaning of the opposite vector, the subtraction of the vector can be converted into the addition of the vector to be implemented

If a and b are opposite vectors, then a=-b, b=-a, a+b=0The inverse of 0 is 0

oa-ob=ba.That is, "a common starting point, pointing to the subtracted".

a=(x1,y1),b=(x2,y2), then a-b=(x1-x2,y1-y2).

Addition and subtraction transformation law: a+(-b)=a-b

Left plus right subtraction, up plus and down subtraction means pointing to the left to move the coordinates plus, to the right move the coordinates minus, up to move the coordinates plus, down to move the Zheng rotation coordinates minus, this is the function image translation law, in line with all the function images. In mathematics, the graph of the function f refers to the set of all ordered pairs (x, f(x)).

Subtraction of vectors. The two vectors share a starting point, connect the end points, and point to the reduced vector.

Subtraction.

A vector equal in length and in the opposite direction is called the opposite vector of a, (a) a, the opposite vector of the zero vector is still a zero vector.

1）a＋(－a)＝(a)＋a＝0（2）a－b＝a＋(－b)。The end point of the subtractive vector is taken as the starting point, and the end point of the subtracted vector is emphasized.