VE230+Homework+1+Fall+2010

VE230+Homework+1+Fall+2010 - 1.4 Verify the back-cab rule...

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VE 230 Electromagnetics I Fall 2010 VE230 Homework 1 (Due 9/17/10) 1.1 Given vectors A = ö x 2 + ö y 4 - ö z 3 , B = ö x 2 + ö y 4 , and C = ö y 2 - ö z 4 , find the following: (a)A and (b)The component of B along C (c) θ AC (d) A ´ B (e) A × B ´ C ( ) (f) A ´ B ´ C ( ) (g) ö x ´ B (h) A ´ ö y ( ) × ö z 1.2 A given line is described by 3 x +2 y = 4 . Vector A starts at the origin and ends at point P on the line such that A is orthogonal to the line. Find an expression for A . 1.3 Convert the coordinates of the following points from Cartesian to cylindrical and spherical coordinates: (a)P 1 (1, 2, 0) (b)P 2 (0, 0, 2) (c) P 3 (1, 1, 3) (d)P 4 (-2, 2, -2)
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Unformatted text preview: 1.4 Verify the back-cab rule of the vector triple product of three vectors in Cartesian coordinates. 1.5 (a) Prove that the equation of any plane in space can be written in the form b 1 x + b 2 y + b 3 z = c . (Hint: Prove that the dot product of the position vector to any point in the plane and a normal vector is a vector.) (b) Find the expression for the unit normal passing through the origin. 1 VE 230 Electromagnetics I Fall 2010 (c) For the plane 3 x- 2 y +6 z = 5 , find the perpendicular distance from the origin to the plane. 2...
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This note was uploaded on 06/24/2011 for the course ECE 203 taught by Professor Wang during the Spring '11 term at University of Michigan.

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VE230+Homework+1+Fall+2010 - 1.4 Verify the back-cab rule...

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