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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.
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![Form 4 [simultaneous equation vs. vector] We use simultaneous equation when we have two unknown to solve. In vector, usually we use simultaneous equation when we have to find the two constant in the two different vector.](https://image.slidesharecdn.com/presentation1-100801085913-phpapp02/85/Presentation1-1-320.jpg)
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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.
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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 representing their sum.
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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.
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.
FORM 5: Linear Law
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.
FORM 3 & FORM 4
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.
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.
More from fatine1232002 (20)
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- 1. Form 4 [simultaneous equation vs. vector] We use simultaneous equation when we have two unknown to solve. In vector, usually we use simultaneous equation when we have to find the two constant in the two different vector.
- 2. Example: Example of simultaneous equation. Subtitude (1) into (2)
- 3. Substitute into (1)
- 4. In the diagram, PQRS is a quadrilateral. PR and QS is a diagonal of the quadrilateral intersection at T. point u lies on PS. It is given that , , and . Given that and where m and n are constant, find the value of m and of n. S R T u P Q Solution: Example of vector.
- 5. Given, Substitute (2) into (1), We use substitute method in simultaneous equation.