1) Draw a picture of two spheres of different sizes being tangent to each other at exactly one point P in R 3 . Do NOT put one sphere inside the other one.2) Suppose we have two surfaces S1 and S2 which intersect at some point P = (x0, y0, z0), 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 TPS1 into the scalar equation for TPS2. Hint: This should be a one-step algebraic transformation based upon using the algebraic definition of parallel vectors.

For part 1 we are given two spheres of different sizes i.e different radius which are tangent to…

Answered: Draw a picture of two spheres of…

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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1) Draw a picture of two spheres of different sizes being tangent to each other at exactly one point P in R ³ . Do NOT put one sphere inside the other one.

2) Suppose we have two surfaces S₁ and S₂ which intersect at some point P = (x₀, y₀, z₀), 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 T_PS₁ and T_PS₂ are the same by transforming the scalar equation for T_PS₁ into the scalar equation for T_PS₂. Hint: This should be a one-step algebraic transformation based upon using the algebraic definition of parallel vectors.

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