Let the position vector (with its tail at the origin) of a moving particle be r = r(t) = t²i - 2tj + (t² + 2t)k, where t represents time. (a) Show that the particle goes through the point (4, -4,8). At what time does it do this? (b) (c) Find the equations of the line tangent to the curve described by the particle and the plane normal to this curve, at the point (4, -4,8). Find the velocity vector and the speed of the particle at time t; at the time when it passes though the point (4, -4,8).

Let the position vector (with its tail at the origin) of a moving particle be r = r(t) = t²i - 2tj + (t² + 2t)k, where t represents time. (a) Show that the particle goes through the point (4, -4,8). At what time does it do this? (b) (c) Find the equations of the line tangent to the curve described by the particle and the plane normal to this curve, at the point (4, -4,8). Find the velocity vector and the speed of the particle at time t; at the time when it passes though the point (4, -4,8).

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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