37. DISCUSS: Same Line: Different Parametric Equations Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equa- tions. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations: Line 1: x = 1 – 1, y = 31, z = -6 + 5t Line 2: x = -1 + 2t, y = 6 – 61, z = 4 – 10r (a) Find two points that lie on Line 1 by setting t = 0 and 1 = 1 in its parametric equations. Then show that these points also lie on Line 2 by finding two values of the parameter that give these points when substituted into the parametric equations for Line 2. (b) Show that the following two lines are not the same by finding a point on Line 3 and then showing that it does not lie on Line 4. Line 3: x = 4, y = 3 – 64, z = -5 + 21 Line 4: x = 8 – 21, y = -9 + 3t, z = 6 – t

37. DISCUSS: Same Line: Different Parametric Equations Every line can be described by infinitely many different sets of parametric equations, since any point on the line and any vector parallel to the line can be used to construct the equa- tions. But how can we tell whether two sets of parametric equations represent the same line? Consider the following two sets of parametric equations: Line 1: x = 1 – 1, y = 31, z = -6 + 5t Line 2: x = -1 + 2t, y = 6 – 61, z = 4 – 10r (a) Find two points that lie on Line 1 by setting t = 0 and 1 = 1 in its parametric equations. Then show that these points also lie on Line 2 by finding two values of the parameter that give these points when substituted into the parametric equations for Line 2. (b) Show that the following two lines are not the same by finding a point on Line 3 and then showing that it does not lie on Line 4. Line 3: x = 4, y = 3 – 64, z = -5 + 21 Line 4: x = 8 – 21, y = -9 + 3t, z = 6 – t

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.FOM: Focus On Modeling: The Path Of A Projectile

Problem 6P: Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as...

See similar textbooks