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A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether or not a line tangent to r(t) = (t², t², t³) at t = 1 will in line through (2,2,3) in the direction = (3,-2,-1). Find the point of inters exists. C. Determine whether particles travelling along a line tangent to r(t) = (t², t², 1 and the line through (2,2,2) in the direction v = (3, —2, −1) would collide not collide if these lines intersect

A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether or not a line tangent to r(t) = (t², t², t³) at t = 1 will in line through (2,2,3) in the direction = (3,-2,-1). Find the point of inters exists. C. Determine whether particles travelling along a line tangent to r(t) = (t², t², 1 and the line through (2,2,2) in the direction v = (3, —2, −1) would collide not collide if these lines intersect

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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3. Suppose that a particle has position function r(t) = (t², t², t³). A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether or not a line tangent to r(t) = (t², t², t³) at t = 1 will intersect the line through (2,2,3) in the direction = (3,-2, -1). Find the point of intersection if it exists. C. Determine whether particles travelling along a line tangent to r(t) = (t², t², t³) at t = 1 and the line through (2,2,3) in the direction = (3,-2,−1) would collide or would not collide if these lines intersect. D. If the speed of the particle is l '(u)|| = √8u² + 9uª, then, use calculus to find a function that represents how far the particle will travel along r(t) = (t², t², t³) for every t > 0.
Transcribed Image Text:3. Suppose that a particle has position function r(t) = (t², t², t³). A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether or not a line tangent to r(t) = (t², t², t³) at t = 1 will intersect the line through (2,2,3) in the direction = (3,-2, -1). Find the point of intersection if it exists. C. Determine whether particles travelling along a line tangent to r(t) = (t², t², t³) at t = 1 and the line through (2,2,3) in the direction = (3,-2,−1) would collide or would not collide if these lines intersect. D. If the speed of the particle is l '(u)|| = √8u² + 9uª, then, use calculus to find a function that represents how far the particle will travel along r(t) = (t², t², t³) for every t > 0.
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