CHAPTER 3: VECTORS NHAA/IMK/UNIMAP.

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CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.

Presentation transcript:

CHAPTER 3: VECTORS NHAA/IMK/UNIMAP

INTRODUCTION Definition 3.1 a VECTOR is a mathematical quantity that has both MAGNITUDE AND DIRECTION VECTOR: represented by arrow where the direction of arrow indicates the DIRECTION of the vector & the length of arrow indicates the MAGNITUDE of the vector. Eg: displacement, velocity, acceleration, force, ect NHAA/IMK/UNIMAP

INTRODUCTION Definition 3.2 a SCALAR is a mathematical quantity that has MAGNITUDE only VECTOR: represented by a single letter s.a, a. Eg: temperature, mass, length area, ect NHAA/IMK/UNIMAP

INTRODUCTION Definition 3.3 A vector in the plane is a directed line segment that has initial point A and terminal point B, denoted by, ; its length is denoted by . Terminal Point, B Initial Point, A Length: NHAA/IMK/UNIMAP

Variation of vectors Definition 3.3 Vectors Negative (Opposite direction but has the same magnitude) Definition 3.4 Two Equal vectors (If and only if they have the same magnitude and direction) Definition 3.5 Addition of vectors The Triangle Law The Parallelogram Law The Sum of a Number of Vectors

Variation of vectors Definition 3.6 Subtraction of vectors Scalar Multiplication of vectors Definition 3.8 Parallel vectors

Components of vectors

Components of vectors

Components of vectors

Magnitude (length) of vectors NHAA/IMK/UNIMAP

Magnitude (length) of vectors NHAA/IMK/UNIMAP

Magnitude (length) of vectors NHAA/IMK/UNIMAP

VECTOR ALGEBRA OPERATIONS Definition : Vector Addition and Multiplication by a Scalar Let and be vectors with k a scalar. ADDITION : SCALAR MULTIPLICATION: NHAA/IMK/UNIMAP

ADDITION and multiplication OF VECTORS NHAA/IMK/UNIMAP

NHAA/IMK/UNIMAP

PROPERTIES OF VECTOR OPERATIONS Let u,v,w be vectors and a,b be scalars: NHAA/IMK/UNIMAP

Unit vectors Definition : if u is a vector, then the unit vector in the direction of u is defined as: A vector which have length equal to 1 is called a unit vector. NHAA/IMK/UNIMAP

Unit vectors NHAA/IMK/UNIMAP