A constant vector field is given by E = -5ap + 10a +3az. Calculatea. The vector component of E at P (5,rad, 3) parallel to the line x =2, z = 3.b. The angle E makes with the surface z = 3 at the point P.Answer:a. -5ayb. 15.0203

Answered: Image /qna-images/answer/f2a93a1a-db66-413d-852f-b940c6aac658.jpg

Answered: a. The vector component of E at P…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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You are given two planes in parametric form, x1 Il : x2 X1 IL : x2=|0 +41 2 + 2 4 X3 where X1 , X2 , X3, 11 , d2,41, H2 E R. Let L be the line of intersection of п and IL. a. Find vectors nj and nɔ that are normals to П and IL respectively and explain how you can tell without performing any extra calculations that II and II, must intersect in a line. b. Find Cartesian equations for П and IL. c. For your first method, assign one of X2 or X3 to be the parameter o and then use your two Cartesian equations for П and II, to express the other two variables in terms of o and hence write down a parametric vector form of the line of intersection L. d. For your second method, substitute expressions for X1 » X and X3 from the parametric form of II, into your Cartesian equation for II, and hence find a parametric vector form of the line of intersection L. e. If your parametric forms in parts (c) and (d) are different, check that they represent the same line. If your parametric forms in parts (c)…
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a. The vector component of E at P (5,rad, 3) parallel to the line x = 2, z = 3. b. The angle E makes with the surface z = 3 at the point P.