"Plane Vectors and Their Linear Operations" Preliminary PPT of plane vectors (subtraction of vectors)

Description

"Plane Vectors and Their Linear Operations" Preliminary PPT of plane vectors (subtraction of vectors)

Part One: Explanation of Curriculum Standards

1. Understand the meaning of opposite vectors and be able to use opposite vectors to express the meaning of vector subtraction.

2. Master the operation of vector subtraction and its geometric meaning, and be able to skillfully perform vector addition and subtraction operations.

3. Be able to make the difference vector of two vectors.

4. Improve mathematical operation ability through the operations and simple applications of vector addition and subtraction.

Plane vectors and their linear operations PPT, part 2 content: independent preview before class

1. Opposite vector

1. Fill in the blanks.

(1) Definition: Given a vector, we call the vector with the opposite direction and equal magnitude to this vector its opposite vector, and the opposite vector of vector a is recorded as -a.

(2) Properties: ① For the opposite vector: a+(-a)=0.

②If a and b are opposite vectors to each other, then a=-b, a+b=0.

③The opposite vector of the zero vector is still the zero vector.

2. Are opposite vectors the same as opposite numbers?

Tip: It’s different. Opposite numbers mean two numbers with opposite signs and equal absolute values. Opposite vectors mean two vectors with opposite directions and equal modulus.

2. Subtraction of vectors

1. Fill in the blanks.

(1) Definition: Generally, given any two vectors a and b on the plane, if the vector x can satisfy b+x=a, then x is called the difference between the vectors a and b, and is recorded as x=a-b.

(2) How to do it: Pick any point O in the plane and calculate (OA) =a, (OB) =b, then the vector a-b=(BA), as shown in the figure.

2. Do it: As shown in the figure, in ▱ABCD, (AB) =a, (AD) =b, use a, b to represent the vectors (AC), (BD), then (AC) =____________, (BD) =____________.

Answer:a+b b-a

Plane vectors and their linear operations PPT, part three: classroom exploration and learning

Vector subtraction

Example 1 Simplification: (1)((AB) ⃗-(CD) ⃗)-((AC) ⃗-(BD)

(2)((AC) ⃗+(BO) ⃗+(OA) ⃗)-((DC) ⃗-(DO) ⃗-(OB)

Solution: (1)((AB) ⃗-(CD) ⃗)-((AC) ⃗-(BD) ⃗)=((AB) ⃗+(BD) ⃗)-((AC) ⃗+(CD) ⃗)=(AD) ⃗-(AD) ⃗=0.

(2)((AC) ⃗+(BO) ⃗+(OA) ⃗)-((DC) ⃗-(DO) ⃗-(OB) ⃗)=((AC) ⃗+(BA) ⃗)-( (OC) ⃗-(OB) ⃗)=(BC) ⃗-(BC) ⃗=0.

Reflect on the commonly used methods of vector subtraction operations

Variation Training 1 Simplify the following formulas:

(1)(AB) ⃗-(AC) ⃗-(DB)

(2)(AB) ⃗+(BC) ⃗-(AD)

(3)(AB) ⃗-(CD) ⃗-(DB)

Solution: (1)(AB) ⃗-(AC) ⃗-(DB) ⃗=(CB) ⃗+(BD) ⃗=(CD)

(2)(AB) ⃗+(BC) ⃗-(AD) ⃗=(AC) ⃗-(AD) ⃗=(DC)

(3)(AB) ⃗-(CD) ⃗-(DB) ⃗=(AB) ⃗+(DC) ⃗+(BD)

=(AB) ⃗+(BD) ⃗+(DC) ⃗=(AC)

The geometric meaning and simple application of vector subtraction

Example 2(1) As shown in Figure 1, in the quadrilateral ABCD, if (AB) ⃗=a, (AD) ⃗=b, (BC) ⃗=c, then (DC) ⃗=()

A.a-b+c B.b-(a+c)

C.a+b+c D.b-a+c

(2) As shown in Figure 2, it is known that the vectors a, b, and c are not collinear, so find the vector a+b-c.

Reflect on two ideas for finding the difference vector between two vectors

1. It can be converted into vector addition, such as a-b, you can first do -b, and then do a+(-b).

2. You can also directly use the triangle rule of vector subtraction, that is, if the starting points of the two vectors coincide, then the difference vector is the vector connecting the end points of the two vectors and pointing to the end point of the vector being subtracted.

Plane vectors and their linear operations PPT, part 4: thinking analysis

Proving Vector Identities - Mathematical Methods

As shown in the figure, O is the circumcenter of △ABC, and H is the orthocenter of △ABC.

Prove as shown in the figure, draw the diameter BD of the circumscribed circle of △ABC,

Connect AD and CD, then (OB) =-(OD) ,DA⊥AB,DC⊥BC.

And because AH⊥BC,CH⊥AB,

So CH∥DA,AH∥DC.

So the quadrilateral AHCD is a parallelogram. So (AH) = (DC) .

And (DC) =(OC) -(OD) =(OC) +(OB) ,

So (OH) =(OA) +(AH) =(OA) +(DC) =(OA) +(OB) +(OC) .

Reflection and understanding: The key to using vector addition and subtraction to prove geometry problems is to fully explore the known conditions and put the unknown vectors in triangles or parallelograms for calculation and representation.

Plane vectors and their linear operations PPT, Part 5: Inspection in class

1. In triangle ABC, (BC) =a, (CA) =b, then (AB) =()

A.a-b B.b-a

C.b+a D.-a-b

Answer:D

2. Which of the following four formulas cannot be reduced to (AD) is ()

A.((AB) +(CD) )+(BC)

B.((AD) +(MB) )+((BC) +(CM) )

C.((MB) +(AD) )-(BM)

D.((OC) -(OA) )+(CD)

Keywords: Free download of PPT courseware for compulsory course II of Mathematics of High School People's Education B version, download of plane vector and its linear operations PPT, download of preliminary PPT of plane vector, download of subtraction of vectors PPT, .PPT format;

For more information about the PPT courseware "Subtraction of Preliminary Plane Vectors and Linear Operation Vectors of Plane Vectors", please click on the PPT tag of "Subtraction of Preliminary Plane Vectors and Linear Operations of Plane Vectors and PPT Vectors".

"Plane Vectors and Their Linear Operations" Preliminary PPT courseware for plane vectors (multiplying vectors and linear operations of vectors):

"Plane Vectors and Their Linear Operations" Plane Vector Preliminary PPT Courseware (Linear Operations of Multiplying Vectors) Part One: Learning Objectives: Understand the concept of multiplied vectors and understand the geometric meaning of multiplied vectors. Understand and master the mixed operations of vectors. Will proceed...

"Plane Vectors and Their Linear Operations" Preliminary PPT courseware for plane vectors (subtraction of vectors):

"Plane Vectors and Their Linear Operations" Plane Vector Preliminary PPT Courseware (Vector Subtraction) Part One Content: Learning Objectives Understand the meaning of opposite vectors, be able to use opposite vectors to tell the meaning of vector subtraction, master the operation of vector subtraction and its geometric meaning , can skillfully...

"Plane Vectors and Their Linear Operations" Preliminary PPT courseware for plane vectors (addition of vectors):

"Plane Vectors and Their Linear Operations" Plane Vector Preliminary PPT Courseware (Vector Addition) Part One Content: Learning Objectives Understand and master the concept of vector addition, understand the geometric meaning of vector addition and its operational laws, master the operation rules of vector addition, and be proficient in it Digging in..

File Info

Update Time: 2024-10-31

This template belongs to Mathematics courseware People's Education High School Mathematics Edition B Compulsory Course 2 industry PPT template

Preview