"End of Chapter Review Improvement Course" Flat Vector Preliminary PPT

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"End of Chapter Review Improvement Course" Flat Vector Preliminary PPT

Comprehensive improvement

Concepts related to plane vectors

Example 1 gives the following proposition:

① A directed line segment is a vector, and a vector is a directed line segment;

② If vector a is parallel to vector b, then the directions of a and b are the same or opposite;

③The vector AB→ is collinear with the vector CD→, then the four points A, B, C, and D are collinear;

④If a∥b, b∥c, then a∥c.

The number of correct propositions is ()

A． 1B． 2

C． 3D． 0

[Analysis] ① Incorrect, vectors can be represented by directed line segments, but vectors are not directed line segments, and directed line segments are not vectors;

②Incorrect, if either a or b is a zero vector, the direction of the zero vector is uncertain, so the directions of the two vectors are not necessarily the same or opposite;

③Incorrect, the straight lines where the collinear vectors are located can coincide or be parallel;

④Incorrect, if b=0, then a and c are not necessarily parallel.

Backwash boost

Three points should be noted about the concept of vectors:

(1) Two characteristics of vectors: they have magnitude and direction. Vectors can be represented by directed line segments and letters, or by coordinates.

(2) Equal vectors are not only equal in modulus, but also in the same direction, so equal vectors must be parallel vectors, but parallel vectors are not necessarily equal vectors.

(3) Vectors are different from quantities. Quantities can be compared in size, but vectors cannot. However, the module of a vector is a non-negative real number and can be compared in size.

Linear operations on plane vectors

Example 2 There are three points A(2,-1), B(1,4), and D(4,-3) on the plane. Point C is on the straight line AB, and AC→=12BC→, connect DC and extend to E , make |CE→|＝

14|ED→|, then the coordinates of point E are ________.

regular method

(1) Vector addition is defined by the triangle rule, and the key point is "connected end to end", that is, AB→+BC→=AC→.

The parallelogram rule for vector addition: move the two vectors to a common starting point and draw a parallelogram for adjacent sides, then the diagonal vectors from the same starting point are the sum of the vectors. Addition satisfies commutative law and associative law.

(2) The essence of vector subtraction is the inverse operation of vector addition, which is the effect of the opposite vector.

(3) Number multiplication operation is to realize the expansion and contraction transformation of the vector length in the same direction or reverse direction through the product of real numbers and vectors.

Keywords: Free download of PPT courseware for compulsory course II of Mathematics of High School People's Education B version, download of PPT for end-of-chapter review and improvement course, download of preliminary flat vector PPT, .PPT format;

For more information about the "End of Chapter Review and Improvement Lesson Plane Vector Preliminary" PPT courseware, please click the End of Chapter Review and Improvement Lesson PPT Plane Vector Preliminary PPT tag.

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Update Time: 2024-10-19

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