[QUESTIONPART5-ABC] Kindly provide the correct and complete solution. (I will like your solution if it is complete + SAMPLE FORMAT IS ALSO PROVIDED IN THE PHOTO BELOW, STRICTLY FOLLOW!) Identify and sketch the graph of the following equations in. In item (c), identify and sketch the graph of the traces aswell.22(a)2x + y + 2z² - 8x - 2y + 4z + 11 = 0(b) x = 1 − log₂y(c)− x + y² + ²/² = 09 Examples:1. Let 2 be a plane containing the point Po(4, -2, -3) and having a normal vectorN = (2,-1,2).The standard equation of the plane 2 is given by 2 (x-4)-1(y + 2) + 2(+3) = 0.So, the general equation of the plane 2 is given by 2x-y+2z-4 = 0.To sketch the graph of the plane, we use the intercepts:2-intercept: 2y-intercept:2-intercept: 2Po2. In geometry, it is known that a plane is uniquely determined by any three noncollinearpoints of the plane.Let I be a plane containing the points P(2,3,0), Q(0,5, -1) and R(1,0,3).To determine the equation of the plane, we need to obtain a normal vector-a vector thatis orthogonal to the plane. This can be obtained by solving for a vector that is orthogonalto vectors determined by points P, Q and R.We consider vectors PQ = (-2,2,-1) and PR = (-1,-3,3). A normal vector to theplane should be orthogonal to both vectors PQ and PR. This can then be obtained usingcross product.XLet N = PQ PR. Vector N is orthogonal to the plane. So, N is a normal vector to I.i jComputing, N=PQ x PR = -2 2k-1=(3,7,8).-1-33Using N as a normal vector and Po any of the three given points, a standard equationcan be obtained. The resulting general equation of plane I is 3x + 7y +82-27 = 0.Verify that points P, Q and R each satisfies the equation.Alternatively, obtain a normal vector to the plane using the cross product of vectors QRand QP. Use this normal vector to obtain a standard equation of the plane. Verify thatthis leads to the same eral equation of plane I.

To Identify and Sketch: (a) 2x2+y2+2z2-8x-2y+4z+11=0. (b) x=1-log2y (c) x=y2+z29 In (c) We have to…

Identify and sketch the graph of the following equations in . In item (c), identify and sketch the graph of the traces as well. 2 (a) 2x² + y² + 2z² 8x - 2y + 4z + 11 = 0 (b) x = 1 - log₂y 2 (c) − x + y + 2²= 0 -

Identify and sketch the graph of the following equations in . In item (c), identify and sketch the graph of the traces as well. 2 (a) 2x² + y² + 2z² 8x - 2y + 4z + 11 = 0 (b) x = 1 - log₂y 2 (c) − x + y + 2²= 0 -

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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