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EE325_Quiz_1_sol_Yilmaz

EE325_Quiz_1_sol_Yilmaz - NAME Solution ˆ 1 Express the...

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NAME: _____________ Solution EE325-Fall 2009 Quiz 1 1) Express the unit vector ˆ x a in cylindrical coordinate system, i.e., in terms of ˆ ˆ ˆ , , , , , . z a a a z ρ φ ρ φ Hint: Dot product of two vectors gives the projection of one vector onto the other. (5 points) ˆ ˆ ˆ cos sin x a a a ρ φ φ φ = 2) Express the following point specified in spherical coordinates in Cartesian coordinates: 3 ( , , ) (2, , ) ( , , ) ? 2 2 r x y z π π θ φ = = (2 points) 3 ( , , ) (2, , ) ( , , ) (0, 2,0) 2 2 r x y z π π θ φ = = 3) Find the vector component of ˆ ˆ ˆ 0.1 0.2 0.3 x y z a a a = + + G that is perpendicular to ˆ ˆ ˆ 10 6 5 x y z a a a = + F . Hint: The result should be a vector. (3 points) See Homework 1 solutions. EE325-Fall 2009 Quiz 1 1) Express the unit vector ˆ x a in spherical coordinate system, i.e., in terms of ˆ ˆ
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