RF/Microwave Engineering and Applications in Energy Systems. Abdullah Eroglu

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a With ampersand c period circ semicolon Subscript y"/>, then find unit vector nor mal to these two vectors.

      Problem 1.4

      If a plane is defined by 3x + 4y + 5z = 10, find the unit vector normal to this plane.

      Problem 1.5

      If two arbitrary vectors are given as and , how can you prove they are perpendicular?

      Problem 1.6

      Calculate the gradients of the following functions.

      1 f = x3y2z

      2  (cylindrical coordinate)

      3 

      Problem 1.7

      Calculate the divergence of the following vectors

      1 

      2 Figure 1.20 Geometry for Problem 1.9.Figure 1.21 Geometry for Problem 1.10.

      3 

      Problem 1.8

      Find the curl of the following vectors (a) K = 3xy²z⁻¹ (b) L = (sin²ϕ)r − r² z cosϕ (c) M = R²sinθ + r(cos ϕ)⁻¹

Problem 1.9

A = y² + x². Verify Stokes' theorem for the geometry given in Figure 1.20.

Problem 1.10

      Prove divergence theorem using the function

and a cube situated at the origin as in Figure 1.21.

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