Explanation Given information : The plane passes through the point ( 1,2,-1 ) and is parallel to the plane 2 x - y + 3 z =1 . Formula used : A plane passes through the point ( α,β,λ ) is given by A ( x − α ) + B ( y − β ) + C ( z − λ ) =0 where A , B , and C are the direction ratios of the normal to the plane. The ratio of direction ratios of two parallel lines is constant. Calculations: The equation of a plane passing through point ( 1,2,-1 ) is A ( x − 1 ) + B ( y − 2 ) + C ( z + 1 ) =0 … (1) The direction ratios of the normal to the plane are A , B , and C . The plane parallel to the plane (1) is 2 x - y + 3 z =1 … (2) The direction ratios of the normal to the plane (1) are A , B , C , and the direction ratios of the normal to the plane (2) are 2,-1, and 3. Since, plane (1) is parallel to plane (2). Therefore, the normals to them also are parallel. Hence, the ratios of their normals is constant, i.e

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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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 9.6, Problem 51PS

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Chapter 9.6, Problem 50PS

Chapter 9.6, Problem 52PS

Chapter 9 Solutions

Student's Solution and Survival Manual for Calculus

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Tofind: The equation of plane passing through a point and parallel to a given plane.

Solution Summary: The author explains the equation of plane passing through a point and parallel to the given plane. The plane passes through the point (1,2,-1).

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