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Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line x=y=z, 45° with the line x=y-z=0 and 0 with the plane x = 0. The distance of the plane from point (2, 1, 1) is 3 units. Find the value of 0 and the equation of the plane.

Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line x=y=z, 45° with the line x=y-z=0 and 0 with the plane x = 0. The distance of the plane from point (2, 1, 1) is 3 units. Find the value of 0 and the equation of the plane.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line x=y=z, 45° with the line x=y=z=0 and 0 with the plane x = 0. The distance of the plane from point (2, 1, 1) is 3 units. Find the value of 0 and the equation of the plane. Prove that for all values of A and μ, the planes 2+2+2-1+2 2x y 2z 2 + ² + ²2-1 + 2( ² - 3 - 4 - 2) = 0 4x 3y 5y 4z a b b C +3=0 intersect on the same line.
Transcribed Image Text:Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line x=y=z, 45° with the line x=y=z=0 and 0 with the plane x = 0. The distance of the plane from point (2, 1, 1) is 3 units. Find the value of 0 and the equation of the plane. Prove that for all values of A and μ, the planes 2+2+2-1+2 2x y 2z 2 + ² + ²2-1 + 2( ² - 3 - 4 - 2) = 0 4x 3y 5y 4z a b b C +3=0 intersect on the same line.
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