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Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z –8 = 0, and (üi) 2x + 35y - 39z + 92 = 0, have a common line of intersection. Prove that the point in %3D which the line 3 e-1 y z- 3 meets the third plane is %3D 1 | equidistant from other two planes.

Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z –8 = 0, and (üi) 2x + 35y - 39z + 92 = 0, have a common line of intersection. Prove that the point in %3D which the line 3 e-1 y z- 3 meets the third plane is %3D 1 | equidistant from other two planes.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that the planes (i) 12x - 15y + 16z – 28 = 0, (ii) 6x + 6y - 7z - 8 = 0, and (iii) 2x + 35y – 39z + 92 = 0, have a common line of intersection. Prove that the point in x-1y 2-3 meets the third plane is 1 which the line - 2 equidistant from other two planes.
Transcribed Image Text:Prove that the planes (i) 12x - 15y + 16z – 28 = 0, (ii) 6x + 6y - 7z - 8 = 0, and (iii) 2x + 35y – 39z + 92 = 0, have a common line of intersection. Prove that the point in x-1y 2-3 meets the third plane is 1 which the line - 2 equidistant from other two planes.
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