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Find the Equation of the Plane Passing Through the Origin and Perpendicular to Each of the Planes X + 2y − Z = 1 and 3x − 4y + Z = 5. - Mathematics

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प्रश्न

Find the equation of the plane passing through the origin and perpendicular to each of the planes x + 2y − z = 1 and 3x − 4y + z = 5.

 
बेरीज

उत्तर

 The equation of any plane passing through the origin (0, 0, 0) is 
a(x0)+b(y0)+c(z0)=0
ax+by+cz=0...(1)
[It is given that (1) is perpendicular to the planes x + 2y - z = 1 and 3x - 4y + z = 5 . Then ,
a+2bc=0...(2)
3a4b+c=0...(3)
 Solving (1), (2) and (3), we get 
|xyz121341|=0
2x4y10z=0
x+2y+5z=0

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पाठ 29: The Plane - Exercise 29.06 [पृष्ठ २९]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 29 The Plane
Exercise 29.06 | Q 7 | पृष्ठ २९

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