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Vectors in the Plane (Zambak).

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Author(s): Ertuðrul Tarhan
Edition: 1
Publisher: Zambak Publishing
Year: 2005

Language: English
Pages: 64

VECTORS IN THE PLANE
1. ANALYSIS OOF VVECTORS
GEOMETRICALLY .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..2
A. BASIC VECTOR CONCEPTS . . . . . . . .2
1. DDirected LLine SSegment . . . . . . . . . . . 2
2. DDefinition oof aa VVector . . . . . . . . . . . . . 3
3. EEqual VVectors . . . . . . . . . . . . . . . . . . . 3
B. VECTOR OPERATIONS . . . . . . . . . . . .4
1. AAddition oof VVectors . . . . . . . . . . . . . . . 4
2. SSubtraction oof VVectors . . . . . . . . . . . . 8
3. MMultiplication oof aa VVector bby aa SScalar . .9
C. PARALLEL VECTORS . . . . . . . . . . . . . .10
1. PParallel VVectors . . . . . . . . . . . . . . . . . .10
2. NNon-PParallel VVectors . . . . . . . . . . . . .11
Activity: Traffic Signs . . . . . . . . . . . . .13
EXERCISES 1 . . . . . . . . . . . . . . . . . . . . .13
2. ANALYSIS OOF VVECTORS
ANALYTICALLY .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..15
A. BASIC CONCEPTS OF VECTORS
IN THE ANALYTIC PLANE . . . . . . . . .15
1. AAxioms . . . . . . . . . . . . . . . . . . . . . . . . .15
2. TThe RRectangular CCoordinate SSystem . .15
3. PPosition VVector . . . . . . . . . . . . . . . . . .16
4. CComponents oof aa VVector . . . . . . . . . . .17
5. EEqual VVectors . . . . . . . . . . . . . . . . . . .18
B. VECTOR OPERATIONS . . . . . . . . . . . .19
1. AAddition oof VVectors . . . . . . . . . . . . . .19
2. SSubtraction oof VVectors . . . . . . . . . . . .20
3. MMultiplication oof aa VVector
by aa SScalar . . . . . . . . . . . . . . . . . . . . .21
4. SStandard BBase VVectors . . . . . . . . . . . .22
C. VECTOR APPLICATIONS . . . . . . . . . . . .24
D. PARALLEL VECTORS . . . . . . . . . . . . . .26
E. LINEAR COMBINATION
OF VECTORS . . . . . . . . . . . . . . . . . . . . .27
1. LLinear CCombination oof VVectors .. .. .. .. .. .. .. .. .. ..27
2. LLinearly DDependent aand
Independent VVectors ((OPTIONAL) .. .. .. .. .. ..29
Activity: Computer Applications . . . . . . .30
EXERCISES 2 . . . . . . . . . . . . . . . . . . . . . . . .30
3. THE DDOT PPRODUCT OOF TTWO
VECTORS .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..33
A. DOT PRODUCT . . . . . . . . . . . . . . . . . . .33
1. PProperties oof tthe DDot PProduct .. .. .. .. .. .. .. .. .. .. ..33
B. ANGLE BETWEEN TWO VECTORS . . . .34
1. AAngle BBetween TTwo VVectors .. .. .. .. .. .. .. .. .. .. .. .. ..34
2. PPerpendicular aand PParallel VVectors .. .. .. .. .. ..36
C. COMPONENT OF
→uu
ALONG
vv →(OPTIONAL) . . . . . . . . . . . . .40
Activity: Projectile Motion in Sport . . . . .43
EXERCISES 3 . . . . . . . . . . . . . . . . . . . . . . . .45
CHAPTER SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . .47
CONCEPT CHECK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
CHAPTER REVIEW TEST 1 . . . . . . . . . . . . . . . . . . . . .48
CHAPTER REVIEW TEST 2 . . . . . . . . . . . . . . . . . . . . .50
ANSWERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55