Explanation Given information : The required line L 1 passes through point ( -1, 3 , 1 ) , and meets the line L 2 : x =2- t , y = 1 − 2 t , z =5+ t orthogonally. Formula used : A line passing through point ( α,β,γ ) and having direction ratios ( a ', b ', c ' ) is given by x − α a ' = y − β b ' = z − γ c ' . Calculations: The line passing through point A ( -1, 3 , 1 ) and having direction ratios ( a ', b ', c ' ) is x + 1 a ' = y − 3 b ' = z − 1 c ' … (1) Let the line (1) meets line L 2 : x =2- t , y = 1 − 2 t , z =5+ t at point B orthogonally. The coordinates of point B are ( 2- t , 1 − 2 t , 5+ t ) . The direction ratios of the line AB are a '=2- t + 1 , b '= 1 − 2 t − 3 , c '=5+ t − 1 or a '=3- t , b '= − ( 2 + 2 t ) , c '=4+ t . The direction ratios of the line L 2 : x =2- t , y = 1 − 2 t , z =5+ t or x − 2 − 1 = y − 1 − 2 = z − 5 1 are a =-1, b = − 2 , c = 1

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ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 9.5, Problem 55PS

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Tofind:The equation of a line that contains a given point and meets another line orthogonally.

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Chapter 9.5, Problem 54PS

Chapter 9.5, Problem 56PS

Chapter 9 Solutions

Calculus

Ch. 9.1 - Prob. 1PS Ch. 9.1 - Prob. 2PS Ch. 9.1 - Prob. 3PS Ch. 9.1 - Prob. 4PS Ch. 9.1 - Prob. 5PS Ch. 9.1 - Prob. 6PS Ch. 9.1 - Prob. 7PS Ch. 9.1 - Prob. 8PS Ch. 9.1 - Prob. 9PS Ch. 9.1 - Prob. 10PS

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Tofind: The equation of a line that contains a given point and meets another line orthogonally.

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