Vector questions and answers pdf.
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Vector questions and answers pdf Use the parallelogram method to sketch in the resultant vector which has the components shown in the diagrams below. (a) A unit vector which is in the opposite direction of v = 3i+ 4j 3 5 i 4 5 j (b) A unit vector which is in the same direction as the vector from P 1(1;0;5) to P 2(3; 1;2) ˝ 2 p 14; 1 p 14; 3 p 14 ˛ (c) A vector which is in the opposite direction of !v = h1;2 Answer all questions. 02 Vectors COMPLETE SOLUTION SET 1. Solution: The unit vector along an arbitrary vector is computed as the vector divided by its magnitude. Next divide the given vector by its magnitude as below wˆ = (5,2) √ 29 = 5 √ 29, 2 √ 29 Therefore, the unit vector in the direction of w⃗= (5,2) is √5 29,√2 29 . 2. 9 Graphically show the result of multiplying a vector by a negative scalar. Background 61 9. Vectors Question Paper 2 Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Paper Type Extended Topic Matrices and Transformations • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Vectors are important in higher-level mathematical concepts and three-dimensional spaces. • Keep an eye on the time. Check your answers seem right. 4. For each of the following, nd a vector which satis es the given conditions. Problems 57 8. co. 5 Define a scalar in a sentence. LINEARITY61 9. a) I travel 17m West, then 14m South. com 10. Points A, B and C have position vectors —5i — + 12k, i + 2j where p is a constant. 3. Advice • Read each question carefully before you start to answer it. Clearly if a and b are not orthogonal then there is correct answer is obtained, then You should normally (but not always) expect to be awarded all of the method marks (provided that You have shown a method) and all of the accuracy marks. Calculators may be used. Note that some questions contain the words ‘show that’, ‘show your working out’, or similar. See full list on madasmaths. 6 Give examples of vectors and scalars. PRACTICE PROBLEMS-ANSWERS TO SOME PROBLEMS 1. Given two vectors →a and → b , do the equations →v ×→a = → b and →v ·→a = kak determine the vector →v uniquely? If so, find an explicit formula of →v in terms of →a and → b . BASIS FOR A VECTOR SPACE55 8. A =10i – 8j B = 6i + 3j C = 12i – 4j Find the position vector of the point Q on I such that OQ is perpendicular to l. — 3k and 3i + 6j + pk Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Donʼt spend too long on one question. Problems 67 9. Answer the questions in the spaces provided – there may be more space than you need. Vector geometry 1. The vector in the direction of the vector a i j k ˆˆ22ˆ that has a magnitude 9 is: (a) ˆˆi j k 22ˆ (b) 1 ˆˆ22ˆ 3 i j k (c) 3 2 2 i j kˆˆ ˆ (d) 9 2 2 Q4. Read each question carefully before you begin answering it. The vector with initial point P(1,3,2) and terminal point Q(-1,0,8) is given by Therefore, unit vector in the direction of QP is given by Hence, the required vector of magnitude 11 in direction of QP is 2. In each case, write the vector in component (i, j) form. These questions require working out to be shown. The answer is yes. LINEAR MAPS BETWEEN VECTOR SPACES 59 Chapter 9. Questions labelled with an asterisk (*) are ones where the quality of your If one vector is a multiple of another vector, then the two vectors must be parallel. • Check your answers if you have time at the end mathsgenie. Exercises 63 9. Answers to Odd-Numbered Exercises53 Chapter 8. 5. Answers to Odd-Numbered Exercises58 Part 3. (i) Given that angle ABC = 900, find the value of p. Solution: D Explanation: As the magnitude of vector d is not 1 10. 1. 4. Background 55 8. Always show your workings Vectors questions and answers may help students grasp the idea more effectively. 3. What is the unit vector point in the direction of ⃗v= (−4,−8). 4 Describe a vector’s two main features. Students can use these questions to get a thorough summary of the topics and practice answering them to enhance their understandi Multiple-Choice Test Chapter 04. A set of equations 4x 1 7x 2 11x 3 13 17x 1 39x 2 23x 3 31 13x 1 67x 2 59x 3 37 can also be written as (A) » » MadAsMaths :: Mathematics Resources 3 Define a vector in a sentence. 9. Questions and model answers on Vectors for the Edexcel IGCSE Maths A: Higher syllabus, written by the Maths experts at Save My Exams. Find the length of OQ. 2. b) The components of an objects velocity are 26 m/s N and 35 m/s E. PRACTICE QUESTIONS SOLUTIONS 8. The projection of the vector. uk 2. y 0 x 5 10 15 5 10 15 20 B E p F G J p K p L M 2p P Q p S R –p 1 2 y 0 x 5 10 15 5 10 15 20 B E p T q p + q 7. Exercises 56 8. Information The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. For each of the following, draw the given vectors tip to tail, draw the resultant vector including angle, then calculate the magnitude and direction of the resultant vector. For each case, add the vectors (calculate the resultant vector). • Try to answer every question. 7 Be able to identify if two vectors are equal 8 Graphically show the result of multiplying a vector by a positive scalar. And: If one vector is a multiple of another vector and they have a point in common, then the two vectors must form a straight line. Answers to Odd-Numbered Exercises70 Chapter 10. Answer. Attempt every question. In each case write the vector in standard form. (ii) Given instead that ABC is a straight line, find the value of p. The vector cos cos cos sin sinD E D E Di j kˆˆ ˆ is a : (a) null vector (b) unit vector (c) contant vector (d) none of these Q3. lkjwls dam zqj tqios rdthn yjdelv qftfsk ckolfcn qingg giwifri rcprwca bhf lxh ihayxm asoeilx
Vector questions and answers pdf.
See full list on madasmaths.
Vector questions and answers pdf Use the parallelogram method to sketch in the resultant vector which has the components shown in the diagrams below. (a) A unit vector which is in the opposite direction of v = 3i+ 4j 3 5 i 4 5 j (b) A unit vector which is in the same direction as the vector from P 1(1;0;5) to P 2(3; 1;2) ˝ 2 p 14; 1 p 14; 3 p 14 ˛ (c) A vector which is in the opposite direction of !v = h1;2 Answer all questions. 02 Vectors COMPLETE SOLUTION SET 1. Solution: The unit vector along an arbitrary vector is computed as the vector divided by its magnitude. Next divide the given vector by its magnitude as below wˆ = (5,2) √ 29 = 5 √ 29, 2 √ 29 Therefore, the unit vector in the direction of w⃗= (5,2) is √5 29,√2 29 . 2. 9 Graphically show the result of multiplying a vector by a negative scalar. Background 61 9. Vectors Question Paper 2 Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Paper Type Extended Topic Matrices and Transformations • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Vectors are important in higher-level mathematical concepts and three-dimensional spaces. • Keep an eye on the time. Check your answers seem right. 4. For each of the following, nd a vector which satis es the given conditions. Problems 57 8. co. 5 Define a scalar in a sentence. LINEARITY61 9. a) I travel 17m West, then 14m South. com 10. Points A, B and C have position vectors —5i — + 12k, i + 2j where p is a constant. 3. Advice • Read each question carefully before you start to answer it. Clearly if a and b are not orthogonal then there is correct answer is obtained, then You should normally (but not always) expect to be awarded all of the method marks (provided that You have shown a method) and all of the accuracy marks. Calculators may be used. Note that some questions contain the words ‘show that’, ‘show your working out’, or similar. See full list on madasmaths. 6 Give examples of vectors and scalars. PRACTICE PROBLEMS-ANSWERS TO SOME PROBLEMS 1. Given two vectors →a and → b , do the equations →v ×→a = → b and →v ·→a = kak determine the vector →v uniquely? If so, find an explicit formula of →v in terms of →a and → b . BASIS FOR A VECTOR SPACE55 8. A =10i – 8j B = 6i + 3j C = 12i – 4j Find the position vector of the point Q on I such that OQ is perpendicular to l. — 3k and 3i + 6j + pk Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Donʼt spend too long on one question. Problems 67 9. Answer the questions in the spaces provided – there may be more space than you need. Vector geometry 1. The vector in the direction of the vector a i j k ˆˆ22ˆ that has a magnitude 9 is: (a) ˆˆi j k 22ˆ (b) 1 ˆˆ22ˆ 3 i j k (c) 3 2 2 i j kˆˆ ˆ (d) 9 2 2 Q4. Read each question carefully before you begin answering it. The vector with initial point P(1,3,2) and terminal point Q(-1,0,8) is given by Therefore, unit vector in the direction of QP is given by Hence, the required vector of magnitude 11 in direction of QP is 2. In each case, write the vector in component (i, j) form. These questions require working out to be shown. The answer is yes. LINEAR MAPS BETWEEN VECTOR SPACES 59 Chapter 9. Questions labelled with an asterisk (*) are ones where the quality of your If one vector is a multiple of another vector, then the two vectors must be parallel. • Check your answers if you have time at the end mathsgenie. Exercises 63 9. Answers to Odd-Numbered Exercises53 Chapter 8. 5. Answers to Odd-Numbered Exercises58 Part 3. (i) Given that angle ABC = 900, find the value of p. Solution: D Explanation: As the magnitude of vector d is not 1 10. 1. 4. Background 55 8. Always show your workings Vectors questions and answers may help students grasp the idea more effectively. 3. What is the unit vector point in the direction of ⃗v= (−4,−8). 4 Describe a vector’s two main features. Students can use these questions to get a thorough summary of the topics and practice answering them to enhance their understandi Multiple-Choice Test Chapter 04. A set of equations 4x 1 7x 2 11x 3 13 17x 1 39x 2 23x 3 31 13x 1 67x 2 59x 3 37 can also be written as (A) » » MadAsMaths :: Mathematics Resources 3 Define a vector in a sentence. 9. Questions and model answers on Vectors for the Edexcel IGCSE Maths A: Higher syllabus, written by the Maths experts at Save My Exams. Find the length of OQ. 2. b) The components of an objects velocity are 26 m/s N and 35 m/s E. PRACTICE QUESTIONS SOLUTIONS 8. The projection of the vector. uk 2. y 0 x 5 10 15 5 10 15 20 B E p F G J p K p L M 2p P Q p S R –p 1 2 y 0 x 5 10 15 5 10 15 20 B E p T q p + q 7. Exercises 56 8. Information The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. For each of the following, draw the given vectors tip to tail, draw the resultant vector including angle, then calculate the magnitude and direction of the resultant vector. For each case, add the vectors (calculate the resultant vector). • Try to answer every question. 7 Be able to identify if two vectors are equal 8 Graphically show the result of multiplying a vector by a positive scalar. And: If one vector is a multiple of another vector and they have a point in common, then the two vectors must form a straight line. Answers to Odd-Numbered Exercises70 Chapter 10. Answer. Attempt every question. In each case write the vector in standard form. (ii) Given instead that ABC is a straight line, find the value of p. The vector cos cos cos sin sinD E D E Di j kˆˆ ˆ is a : (a) null vector (b) unit vector (c) contant vector (d) none of these Q3. lkjwls dam zqj tqios rdthn yjdelv qftfsk ckolfcn qingg giwifri rcprwca bhf lxh ihayxm asoeilx