EEE224_Fall09_Lecture2 - Vector Vector has both magnitude...

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1 Vector Vector has both magnitude and direction in space. A a A A ˆ = r A A = r ˆ A A a A = r r Magnitude of the vector A r Unit vector in the direction of A r A r ˆ A a A A = r Falling Snowflakes Velocity vector
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2 Dot (Scalar) Product ˆ A A Aa = ˆ B BB a = AB θ AB BCos A A A B A B A B A B A B A r r r r r r r r r r r r r = = = // 0 Result: scalar !
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3 Cross (Vector) Product // 0 ˆ N AB A BA B a A B ⇔× = ⊥⇔× = r r rr r rrr Result: vector ! Right Hand rule in finding the direction of cross-product.
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4 (Geometrical Interpretation) Magnitude of the cross product is the area of the parallelogram formed by the two vectors. area Cross (Vector) Product
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5 Coordinate Systems 3 PRIMARY “ORTHOGONAL” COORDINATE SYSTEMS: • CARTESIAN • CYLINDRICAL • SPHERICAL Choice is based on symmetry of problem Examples: Sheets - CARTESIAN Wires/Cables - CYLINDRICAL Spheres - SPHERICAL (coordinates mutually perpendicular)
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6 Spherical Coordinates Cylindrical Coordinates Cartesian Coordinates P (x,y,z) P (R, Θ , Φ ) P (r, Φ , z) x y z P(x,y,z) Φ z r x y z P(r, Φ , z) θ Φ R z y x P(R, θ , Φ ) Coordinate Systems
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7 Cartesian Coordinate System
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This note was uploaded on 01/07/2011 for the course EE 209 taught by Professor Alexander during the Spring '10 term at Middle East Technical University.

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EEE224_Fall09_Lecture2 - Vector Vector has both magnitude...

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