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* (b) Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.

* (b) Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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Please solve part(b) only. Thx.

6. (a) Let I be an interval and Ti(t) = (x₁(t), y₁ (t), 2₁ (t)) and F₂(t) = (x₂ (t), y₂2(t), Z₂ (t)), where t = I, be two differentiable curves in R³ Show that i. ii. d ·(F₁(t) · r₂(t)) = r²'₁(t) · F₂(t) + r₁(t) · r²¹₂ (t) dt d (F₁(t) × F₂(t)) = r₁(t) × F₂2(t) + F₁ (t) × √₂ (t) dt (b) * Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t€ I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.
Transcribed Image Text:6. (a) Let I be an interval and Ti(t) = (x₁(t), y₁ (t), 2₁ (t)) and F₂(t) = (x₂ (t), y₂2(t), Z₂ (t)), where t = I, be two differentiable curves in R³ Show that i. ii. d ·(F₁(t) · r₂(t)) = r²'₁(t) · F₂(t) + r₁(t) · r²¹₂ (t) dt d (F₁(t) × F₂(t)) = r₁(t) × F₂2(t) + F₁ (t) × √₂ (t) dt (b) * Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t€ I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.
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