Find the equation of the plane passing through the origin and is perpendicular to the plane x+2y-z-1=0 and 3x-4y+z-5=0.
Solution:
Plane is passing through the origin(0,0,0) :
A(x-x1)+B(y-y1)+C(z-z1)=0
Here x1 = 0 , y1 = 0 and z1 = 0 :
Ax+By+Cz=0 ...(1)
Now from the equations
x+2y-z-1=0 and 3x-4y+z-5=0
1A+2B-C=0
3A-4B+C=0
(A/2-4)-(B/1+3)+(C/-4-6)=K
(A/-2)=-B/4=-C/10=K
So,
A = -2K , B = -4K and C = -10K
Putting values in eq(1) we get,
-2Kx-4ky-10kz = 0
x+2y+5z = 0 .
The equation of plane is x+2y+5z=0 .
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