Vector Analysis Material

1. By Prof. Hitesh Dholakiya
Basics of Vector,
Triangular, Parallelogram
& polygon law
Electromagnetics
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Engineering Funda Android App Electromagnetic Theory YT Playlist

2. Basics of Vector
Triangular Law
Resultant of two vector
Parallelogram Law
Outlines of Session
Polygon Law
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Engineering Funda Android App Electromagnetic Theory YT Playlist

3. Basics of Vector
❖ Difference between vector and scalar
Scalar Vector
1. The quantities which has magnitude and direction are
vector quantities
1. The quantities which has only magnitude, and no
direction, are scalar quantities
2. The vector quantities are more than one dimensional
quantities
2. The scalar quantities are one dimensional
quantities
3. The vector can not be divided with another vector
quantities
3. The scalar can be divided with another scalar
quantities
4. Number (Magnitude), direction (Unit vector) and unit
is required to represent vector quantities
4. Number (Magnitude) and unit is only required to
represent scalar quantities
5. E. g. Velocity, Force
5. E. g. Mass, Time
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Engineering Funda Android App Electromagnetic Theory YT Playlist

4. Basics of Vector
❖ Representation of vector
❖ Magnitude of vector
❖ Unit vector
Ԧ
𝐴 = 𝐴𝑥 Ƹ
𝑖 + 𝐴𝑦 Ƹ
𝑗 + 𝐴𝑧
෠
𝑘 Ԧ
𝐴 = (𝐴𝑥, 𝐴𝑦, 𝐴𝑧)
𝐴 = Ԧ
𝐴 = 𝐴𝑥
2
+ 𝐴𝑦
2
+ 𝐴𝑧
2
෡
𝑖𝐴 =
Ԧ
𝐴
Ԧ
𝐴
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5. Law of Triangle
Ԧ
𝐴
𝐵
Ԧ
𝐶
Ԧ
𝐴
𝐵
Ԧ
𝐶
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6. Resultant of two vector
Ԧ
𝐴
𝐵
Ԧ
𝐶
𝑨 𝐜𝐨𝐬 𝜽
𝑨 𝐬𝐢𝐧 𝜽
❑ As Pythagoras theorem
𝐶2 = (𝐵 + 𝐴 cos 𝜃)2+(𝐴 sin 𝜃)2
𝐶2 = 𝐵2 + 2𝐴𝐵 cos 𝜃 + (𝐴 cos 𝜃)2+(𝐴 sin 𝜃)2
𝐶2 = 𝐵2 + 2𝐴𝐵 cos 𝜃 + 𝐴2
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7. Law of Parallelogram
Ԧ
𝐴
𝐵
Ԧ
𝐶
Ԧ
𝐴
𝐵
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8. Law of Polygon
Ԧ
𝐴
𝐵
Ԧ
𝐶
𝐷
𝐸
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