Problem 3.2 Lines and planes in R³ Consider the plane described by = 4. 2x - 3y + 6z = a) Calculate a unit vector normal to the plane. b) Determine the distance from the origin of the coordinate system (0, 0, 0) to the plane. Provide a sketch. c) Find the angle = [0, π/2] between the plane given by eq. (4) and another plane with equation 3x -z = 0. (4) Provide a sketch. d) Consider the line parametrized by x = 1+ t, y = 2-t, Calculate the point where the line and the plane (eq. (4)) intersect. Find the angle € [0, π/2] between the line and the plane. Provide a sketch. z = 4t

Problem 3.2 Lines and planes in R³ Consider the plane described by = 4. 2x - 3y + 6z = a) Calculate a unit vector normal to the plane. b) Determine the distance from the origin of the coordinate system (0, 0, 0) to the plane. Provide a sketch. c) Find the angle = [0, π/2] between the plane given by eq. (4) and another plane with equation 3x -z = 0. (4) Provide a sketch. d) Consider the line parametrized by x = 1+ t, y = 2-t, Calculate the point where the line and the plane (eq. (4)) intersect. Find the angle € [0, π/2] between the line and the plane. Provide a sketch. z = 4t

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter12: Conic Sections

Section12.CR: Chapter Review

Problem 6CC

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