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).
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter6: Rates Of Change
Section6.1: Velocity
Problem 12SBE
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