دانلود کتاب Vectors in the Plane (Zambak).

فهرست مطالب :

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