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प्रश्न
Find the equation of the plane passing through the intersection of the planes: x + y + z + 1 = 0 and 2x -3y + 5z -2 = 0 and the point ( -1, 2, 1 ).
उत्तर
Equation of required plane passing through the intersection of the planes x + y + x + 1 = 0
and 2x - 3y + 5y - 2 = 0 is
`(x + y + z + 1) + lambda (2x - 3y + 5z - 2) = 0` .....(1)
It passes through (-1, 2, 1)
∴ `(-1 + 2 + 1 + 1) + lambda(-2 - 6 + 5 - 2) = 0`
`3 + lambda(-5) = 0`
`lambda = 3/5`
In equation (1)
`(x + y + z + 1) + 3/5 (2x - 3y + 5z - 2) = 0`
`5x + 5y + 5z + 5 + 6x - 9y + 15 z - 6 = 0`
11x - 4y + 20z - 1 = 0
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संबंधित प्रश्न
Find the equation of the plane passing through the interesection of the planes 2x + 2y -3z -7 =0 and 2x +2y - 3z -7=0 such that the intercepts made by the resulting plane on the x - axis and the z - axis are equal.
The distance of the point (1, 1, 9) from the point of intersection of the line `(x - 3)/1 = ("y" - 4)/2 = ("z" - 5)/2` and the plane x + y + z = 17 is ______.
