FORM 3 & FORM 4
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This document discusses the relationships between various mathematical concepts and the topic of vectors, specifically addition and subtraction of vectors. It provides examples of how polygons, parallel lines, algebraic expressions, and straight lines all relate to vectors. Polygons and parallel lines can be used to understand vector addition and subtraction through laws like the parallelogram law. Algebraic expressions allow expressing vectors in terms of other vectors. And vectors are straight lines with direction and magnitude, making straight lines a basic concept for understanding vectors.
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The document provides guidelines and prompts for journal entries on geometry concepts. It includes 30 prompts asking the student to describe key geometry terms and concepts like points, lines, planes, angles, transformations, congruence, and more. It also prompts the student to provide examples for each term or concept described. The prompts cover topics including geometric shapes, formulas, theorems, and problem-solving processes. The student is awarded points for fully answering each prompt.
1 linear algebra matrices
Linear algebra covers matrices, vectors, determinants, and linear systems. Matrices and vectors are the main tools of linear algebra and allow large amounts of data to be expressed concisely. Chapter 7 introduces matrices and vectors, focusing on addition and scalar multiplication. It also covers solving systems of linear equations using Gaussian elimination and properties of the solutions.
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Derivación e integración de funciones de varias variables
Derivación e integración de funciones de varias variables
Brief review on matrix Algebra for mathematical economics
Brief review on matrix Algebra for mathematical economics
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Appendix 2 baru
This document contains 4 math problems involving vectors: 1) drawing vectors given vector a and b; 2) using the parallelogram law to find the resultant vector of vectors a and b; 3) determining vectors in a triangle given the midpoint and two other vectors; 4) determining vectors in parallelograms given two initial vectors. It provides diagrams and asks to determine various vectors in terms of the given vectors.
Appendix 1 baru
There are two methods for adding vectors: the parallelogram rule and the triangle rule. The parallelogram rule involves translating the vectors tail-to-tail to form the sides of a parallelogram, where the diagonal lines represent the sum vector. The triangle rule places the tail of one vector at the head of the other to form a triangle, where the third side of the triangle is the sum vector. Both methods are equivalent and result in the sum vector having the same magnitude and direction regardless of the order of the original vectors.
Presentation1
Simultaneous equations are used to solve for two unknowns, such as finding the two constants in two vectors. An example problem finds the values of m and n given vectors for points P, Q, R, and S of a quadrilateral, where the vectors are defined in terms of constants m and n. The solution uses the substitute method for simultaneous equations by substituting equation (2) into equation (1) to find the values of m and n.
Appendix 2
The document describes a diagram with vectors a and b. Vector a has length PQ which is 4a, and vector b has length SP which is 3b. The question asks to determine the vectors a + b, RQ, and PS in terms of a and b using properties of parallelograms and midpoints. It also asks to determine the vectors PQ and PT in another diagram where PQST and PQRS are parallelograms with sides PQ = 9p and PT = 6q.
Appendix 1
There are two methods for adding vectors: the parallelogram rule and the triangle rule. The parallelogram rule involves translating the vectors tail-to-tail to form the sides of a parallelogram, where the diagonal lines represent the sum of the vectors. The triangle rule places the tail of one vector at the head of the other to form the sides of a triangle, where the third side of the triangle is the sum of the vectors. Both methods are equivalent and result in the commutative property of vector addition where the order of the vectors does not matter.
Baru matrices
Matrices and vectors can be added or subtracted if they are in the same order. Any matrix can be multiplied by a constant. A vector can be represented as the sum of its horizontal and vertical components multiplied by unit vectors. Both matrices and vectors can be added if they are in the same order.
Topic 1 math (3)
This document discusses how polygons relate to vectors. Polygons can be used to add and subtract vectors using parallelogram and triangle laws. Examples show how vectors can be represented by the sides of polygons, allowing vectors to be easily visualized and understood when solving problems. Polygons are therefore closely related to the topic of vectors in physics and mathematics.
Form 5 (variation vs
This document discusses using the concept of joint variant to write an equation relating variables x, y, and z as y=ax+bz when two vectors p and q are parallel. It provides an example problem to find the possible value of x when p and q are parallel vectors.
Baru matrices
Matrices and vectors can be added or subtracted if they are in the same order. Any matrix can be multiplied by a constant. A vector can be represented as the sum of its horizontal and vertical components multiplied by unit vectors. Both matrices and vectors can be added if they are in the same order.
Topic 1
This document discusses how polygons relate to vectors. Polygons can be used to add and subtract vectors using parallelogram and triangle laws. Examples show how vectors can be represented by the sides of polygons, allowing vectors to be easily visualized and manipulated for problems involving addition and subtraction. Polygons thus provide a useful tool for understanding vector operations.
Linear Equations
This document discusses the relationship between linear algebraic expressions and vectors. A linear algebraic expression consists of two or more linear algebraic terms combined using addition, subtraction, or both. An example problem involves a triangle PQR with midpoint S, where PS = 4a and PR = 3b. Students are asked to write vectors in terms of a and b, showing how linear algebraic expressions are used to represent vectors. The document notes that many vector problems involve algebraic expressions, demonstrating the connection between linear equations and vectors.
Tmp2023
This document discusses how integers are related to vectors and how understanding integers can help students learn vectors. It explains that integers, like vectors, have positive and negative values that represent direction. Subtracting vectors is the same as adding the negative of the second vector, and changing a vector's direction requires applying a negative sign. Mastering the concept of positive and negative integers will therefore help students grasp the similar concept of direction for vectors.
Concept Map
Vectors are quantities that have both a magnitude and a direction. Vectors can be represented as an arrow with a length representing the magnitude and the direction it points representing the direction. The magnitude of a vector is commonly represented by its length and the direction is represented by the angle it makes with the x-axis.
Vector
When two variables are related linearly, plotting their values results in a straight line. This straight line of best fit can be used to add or subtract linear relationships, whether the lines are parallel or non-parallel. Vectors can be added by treating the linear lines of best fit for each variable as vectors, with the resultant vector determined by the sums of the components.
Vector
When two variables are related linearly, plotting their values results in a straight line. This straight line of best fit can be used to add or subtract linear relationships, whether the lines are parallel or non-parallel. Vectors can be added by treating the linear lines of best fit for each variable as vectors, with the resultant vector representing their sum.
Presentation1
Simultaneous equations are used to find two unknowns when given two equations. In vectors, simultaneous equations are used to find two constants in two vector equations. This example shows finding the constants m and n given two vector equations relating points P, Q, R, S, and u of a quadrilateral. The values of m and n are found by substituting one vector equation into the other.
Form 5 (variation vs
This document discusses using the concept of joint variant to write an equation relating variables x, y, and z as y=ax+bz when two vectors p and q are parallel. It provides an example problem to find the possible value of x when given vectors p and q are parallel.
Presentation1
Simultaneous equations are used to find two unknowns when there are two equations. In vectors, simultaneous equations are used to find two constants in two vector equations. The example problem gives two vector equations involving points P, Q, R, S, and T on a quadrilateral, with constants m and n, and asks to find the values of m and n by substituting one equation into the other.
Form 3 and Form 4
This document discusses the relationships between various geometry and algebra topics and the topic of vectors, specifically addition and subtraction of vectors. Polygons, parallel lines, algebraic expressions, and straight lines are all related to vectors because vectors represent straight lines with direction and magnitude. Examples are given of using concepts like the parallelogram law, triangle law, and algebraic expressions to solve vector addition and subtraction problems.
Ratio, Rate and Proportion
The document discusses the definition of ratios and how they relate to vectors. It defines a ratio as the comparison between two quantities that have the same unit. An example shows writing the ratio of 3000 m to 1500 m as 2:1. Ratios are related to vectors because vector problems can use ratios to determine unknown quantities, like using the ratio of 4 PS to SQ to find other vector quantities in a triangle diagram. Mastering ratios is important for understanding vectors since vector concepts apply the ratio concept.
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FORM 3 & FORM 4
- 1. TING. 3 (TOPIC 1) POLygon II
- 15. Expand single bracket with one term
- 16. Expand and multiply two algebraic terms with fraction Thus, as we can see from the example above subtopic addition and subtraction of vector is connected to the algebraic expression as we always use to solve problem relate to vector
- 20. SOLUTION: Resultant vector Subtraction of vector Thus, the straight line is the basic concept of vector. By knowing the knowledge of straight line, we know the direction and magnitude of the vector that can be used in the subtopic (addition and subtraction of vector). That why, STRAIGHT LINE is important to vector E F G H