Chapter One: Vector Analysis The use of vectors and vector analysis ...

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Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department Example: Let , calculate the dot product of with itself: ∙ ∙ ∙ ∙ ∙ ∙ 2 This is the law of cosine. 4‐ Cross product of two vectors (Vector Product): where is a unit vector, pointing perpendicular to the plane of and . (the direction pointed by right‐hand rule). Right‐hand rule: Let your finger point in the direction of the first vector and curl around (via the smaller angle) toward the second; then your thumb indicates the direction of . 0 Vector Algebra: Let , , and be unit vectors parallel to the , , and respectively. An arbitrary vector can be expanded in term of these basis vectors: The numbers , , and are called components of . ∙ ∙ ∙ ∙ ∙ ∙ 1 2
Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department ∙ ∙ ∙ 0 ∙ || ∙ ; ∙ ; ∙ In the case of cross product: Therefore: 0 This cumbersome expression can be written as a determinant: Where is perpendicular to both and . Prove of dot product rule: , , 3
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Chapter One: Vector Analysis The use of vectors and vector analysis ...

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