lollipoph uhjim
Vectors in Two and Three Dimensions
Print References
1. H2 Mathematics for ‘A’ Level Volume 1, Federick Ho, David Khor, Yui-P’ng Lam, B.S. Ong
2. Core Maths for Advanced Level (2000), L. Bostock & S. Chandler.
3. Pure Mathematics (2000), A. Martin, K. Brown, P. Rigby, S. Riley.
Non Print References
1. http://www.geocities.com/h2maths
Objective: At the end of the chapter, students should be able to
1. understand the geometrical and physical interpretations of two and three dimensional vectors, and use standard notations for vectors;
2. understand and use the fact that ;
3. carry out addition and subtraction of vectors, multiplication of a vector by a scalar, and interpret these operations in geometrical terms;
4. use position vectors to denote the locations of points in two and three dimensions;
5. express a displacement vector in terms of the position vectors of its end points, e.g. =;
6. distinguish between position vectors and displacement vectors using practical examples;
7. calculate the magnitude of a vector given in component form;
8. use the displacement vector to calculate the distance between two points and ;
9. understand the concept of a unit vector;
[Note: Vectors parallel to a unit vector a can be written in the form ka, where k is the length of the vector.]
10. find the unit vector of a directed line segment;
11. determine whether three points with given coordinates are collinear;
12. use the ratio theorem to find the position vector of a point that divides a line segment in a given ratio;
13. understand that the scalar product can be expressed as or ;
14. understand that the vector product can be expressed as , where is a unit vector perpendicular to a and , or
;
15. know the difference in properties between scalar and vector products;
16. use the scalar product to find the magnitude of a vector, determine if two vectors are perpendicular, calculate the angle between two
Print References
1. H2 Mathematics for ‘A’ Level Volume 1, Federick Ho, David Khor, Yui-P’ng Lam, B.S. Ong
2. Core Maths for Advanced Level (2000), L. Bostock & S. Chandler.
3. Pure Mathematics (2000), A. Martin, K. Brown, P. Rigby, S. Riley.
Non Print References
1. http://www.geocities.com/h2maths
Objective: At the end of the chapter, students should be able to
1. understand the geometrical and physical interpretations of two and three dimensional vectors, and use standard notations for vectors;
2. understand and use the fact that ;
3. carry out addition and subtraction of vectors, multiplication of a vector by a scalar, and interpret these operations in geometrical terms;
4. use position vectors to denote the locations of points in two and three dimensions;
5. express a displacement vector in terms of the position vectors of its end points, e.g. =;
6. distinguish between position vectors and displacement vectors using practical examples;
7. calculate the magnitude of a vector given in component form;
8. use the displacement vector to calculate the distance between two points and ;
9. understand the concept of a unit vector;
[Note: Vectors parallel to a unit vector a can be written in the form ka, where k is the length of the vector.]
10. find the unit vector of a directed line segment;
11. determine whether three points with given coordinates are collinear;
12. use the ratio theorem to find the position vector of a point that divides a line segment in a given ratio;
13. understand that the scalar product can be expressed as or ;
14. understand that the vector product can be expressed as , where is a unit vector perpendicular to a and , or
;
15. know the difference in properties between scalar and vector products;
16. use the scalar product to find the magnitude of a vector, determine if two vectors are perpendicular, calculate the angle between two