*MULTIVARIABLE CALCULUS, COLLEGE LEVEL VECTORS CALCULUS. 9. On the last day of class, we described how two curves in R? being tangent to each othercorresponded to their normal vectors being parallel (and this helped explain why Lagrangemultipliers work). Now we try to generalize this idea of tangency in various ways.(а)exactly one point P in R³. Do NOT put oe sphere inside the other one.Draw a picture of two spheres of different sizes being tangent to each other at(b)(xo, Y0, zo), and further suppose that the normal vectors n1 = (a1,b1, c1) (for S1) andn2 = (a2, b2, c2) (for S2) at P are parallel (and non-zero). Prove that the tangent planesTpS1 and TpS2 are the same by transforming the scalar equation for TpSı into the scalarequation for TPS2. Hint: This should be a one-step algebraic transformation based uponusing the algebraic definition of parallel vectors.Suppose we have two surfaces S1 and S2 which intersect at some point P Based on what we have so far, we will say two surfaces S1 and S2 are tangent to each otherat an intersection point P when they have parallel normal vectors at P, which is the sameas saying that they have the same tangent plane at P.If our tangent surfaces are graphs S1 =(c)what can you say about the linearization functions Lpf1(x, y)one-to-two sentence explanation for your claim.(graph of f1(x, y)) and S2 = (graph of f2(x, y)),and Lpf2(x, y)? Provide a

a) The objective is to draw two spheres of different sizes tangent to each other at exactly one…

Answered: (a) exactly one point P in R³. Do NOT…

(a) exactly one point P in R³. Do NOT put one sphere inside the other one. Draw a picture of two spheres of different sizes being tangent to each other at

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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Question

*MULTIVARIABLE CALCULUS, COLLEGE LEVEL VECTORS CALCULUS.

9. On the last day of class, we described how two curves in R? being tangent to each other
corresponded to their normal vectors being parallel (and this helped explain why Lagrange
multipliers work). Now we try to generalize this idea of tangency in various ways.
(а)
exactly one point P in R³. Do NOT put oe sphere inside the other one.
Draw a picture of two spheres of different sizes being tangent to each other at
(b)
(xo, Y0, zo), and further suppose that the normal vectors n1 = (a1,b1, c1) (for S1) and
n2 = (a2, b2, c2) (for S2) at P are parallel (and non-zero). Prove that the tangent planes
TpS1 and TpS2 are the same by transforming the scalar equation for TpSı into the scalar
equation for TPS2. Hint: This should be a one-step algebraic transformation based upon
using the algebraic definition of parallel vectors.
Suppose we have two surfaces S1 and S2 which intersect at some point P

Based on what we have so far, we will say two surfaces S1 and S2 are tangent to each other
at an intersection point P when they have parallel normal vectors at P, which is the same
as saying that they have the same tangent plane at P.
If our tangent surfaces are graphs S1 =
(c)
what can you say about the linearization functions Lpf1(x, y)
one-to-two sentence explanation for your claim.
(graph of f1(x, y)) and S2 = (graph of f2(x, y)),
and Lpf2(x, y)? Provide a

Calculus that deals with differentiation and integration of the vector field in three-dimensional Euclidean space. It deals with quantities that have both magnitude and direction.

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