# Find the equation of the plane through the intersection of the planes 3x" "" "y" "+" "2z" "" "4" "=" "0 and x" "+" "y" "+" "z" "" "2" "=" "0 and t

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Find the equation of the plane through the intersection of the planes 3x" "" "y" "+" "2z" "" "4" "=" "0 and x" "+" "y" "+" "z" "" "2" "=" "0 and the point (2, 2, 1).

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The equaiton of the plane passing thorugh the intesection 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)
Now, this plane passes through the point (2,2,1)
therefore" "[3(2) +2(2) -1+1] + lambda (2+2+1-2) = 0
10 + 3lambda = 0
therefore" "lambda = (-10)/(3)
Putting the value of lambda in equation (1) , we get
(3x + 2y -z+1) (10)/(3) (x+y +z -2) = 0
rArr" " 9x + 6y - 3z + 3 - 10y - 10z + 20 = 0
rArr" "x + 4y + 13z - 23 =0
Which is the equaiton of required plane.