2026 Chp 1A (Student) - JPJC

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2026 Chapter 1(a) Vectors − Vector Algebra & Scalar Product / Pg 1 Chapter 1: Vectors Content Outline I. Basic properties of vectors in two- and three dimensions Include: • addition and subtraction of vectors, multiplication of a vector by a scalar, and their geometrical interpretations • position vectors, displacement vectors and direction vectors • magnitude of a vector • unit vectors • distance between two points • collinearity • use of the ratio theorem in geometrical applications II. Scalar and vector products in vectors Include: • concepts of scalar product and vector product of vectors and their properties • calculation of the magnitude of a vector and the angle between two vectors • geometrical meanings of ˆan  and ˆan , where ˆn is a unit vector Exclude triple products a • b × c and a × b × c. III. Three-dimensional vector geometry Include: • vector and cartesian equations of lines and planes • finding the foot of the perpendicular and distance from a point to a line or to a plane • finding the angle between two lines, between a line and a plane, or between two planes • relationships between (i) two lines (coplanar or skew) (ii) a line and a plane (iii) two planes Exclude: • finding the shortest distance between two skew lines • finding an equation for the common perpendicular to two skew lines

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2026 Chapter 1(a) Vectors − Vector Algebra & Scalar Product / Pg 2 References • Websites (1) http://www.h2maths.site (2) https://www.mathsisfun.com/algebra/vectors.html • Books (1) Ho Soo Thong, Tay Yong Chiang & Koh Khee Meng, “College Mathematics Syllabus C Volume 1”, Pan Pacific Publications, Call Number: HO510 (2) Pure Mathematics by Alan Sherlock, Elizabeth Roebuck, Timothy Heneage, Shirley Beck: Chapter 16 (3) Pure Mathematics 2 by L Bostock, S Chandler: Chapter 5 (4) My First Step in using TI-84 Plus CE for H1 and H2 Math by Attal Lam Chapter 1(a): Vector Algebra and Scalar Product 1. Introduction Pre-requisite: GCE “O” Level Elementary Mathematics – 2-dimensional vectors • A scalar quantity is one that is fully defined by magnitude alone, e.g. length, distance, speed. • A vector quantity is one that has both magnitude and direction, e.g. force, displacement, velocity. Geometrical Representation A vector a (directed from P to Q) may be represented geometrically by a directed line PQ . Notation: , or PQ a a   (in the direction from P to Q) 2. 2-Dimensional / 3-Dimensional Vectors Examples of 2D vectors: 1 1   , 4 2 −  . Examples of 3D vectors: 1 1 4    , 4 2 0 −   . Column vector form Q P a 

Jurong Pioneer Junior College H2 Mathematics (9758) JC1-2026 Chapter 1(a) Vectors − Vector Algebra & Scalar Product / Pg 3 Geometrical Rep