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प्रश्न
Find the equation of the plane passing through the intersection of the planes 3x + 2y – z + 1 = 0 and x + y + z – 2 = 0 and the point (2, 2, 1).
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उत्तर
The equation of plane passing through the intersection of the planes 3x + 2y – z + 1 = 0 and x + y + z – 2 = 0 is
`3x + 2y – z + 1)+lambda( x + y + z – 2)=0` ...........(1)
It passes through the point (2, 2, 1)
`(6+4-1+1)+lambda(2+2+1-2)=0`
`10+3lambda=0`
`lambda=-10/3`
Now,
`(3x+2y-z+1)+(-10/3)(x+y+z-2)=0` .......[from(1)]
`9x+6y-3z+3-10x-10y-10z+20=0`
`-x-4y-13z+23=0`
The equation of plane is `x+4y+13z=23`
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