I+t #1 Let r(t)=(x(t), y(t), z(t)) = (1-{², t- ½, ±). (a) Find the moment of time to and the point Po on the curve r(t) when the tangent line to the curve is perpendicular to the plane z=8x-8y+9. Hint. The tangent vector v(t) = r' (to) to the curve must be parallel to the normal vector n to the given plane, hence one of these two vectors is a scalar multiple of the other. Set and solve a system of equations to find to first. (b) Find the tangent line as in part (a).
I+t #1 Let r(t)=(x(t), y(t), z(t)) = (1-{², t- ½, ±). (a) Find the moment of time to and the point Po on the curve r(t) when the tangent line to the curve is perpendicular to the plane z=8x-8y+9. Hint. The tangent vector v(t) = r' (to) to the curve must be parallel to the normal vector n to the given plane, hence one of these two vectors is a scalar multiple of the other. Set and solve a system of equations to find to first. (b) Find the tangent line as in part (a).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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what's the final answer to a and b?
Transcribed Image Text:I+t
#1 Let r(t)=(x(t), y(t), z(t)) = (1-{², t- ½, ±).
(a) Find the moment of time to and
the point Po on the curve r(t) when the
tangent line to the curve is perpendicular
to the plane z=8x-8y+9. Hint.
The tangent vector v(t) = r' (to) to the
curve must be parallel to the normal
vector n to the given plane, hence
one of these two vectors is a scalar
multiple of the other. Set and solve
a system of equations to find to first.
(b) Find the tangent line as in part (a).
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