Question

Find the Cartesian equation of the plane through the points(1,2,3)(2,3,1)and perpendicular to the plane 3x-2y+4z-5=0

Answer 1

Answer:

let the drs of normal of plane be a,b,c

then equation of plane is ax+by+cz=0

we can also write the equation as

  a(x-1)+b(y-2)+c(z-3)=0 ----(1)  (as this plane passes through (1,2,3)

 as this plane also passes through (2,3,1)

  substitute (2,3,1) in (1)

we get a+b-2c=0-----(2)

 as this plane is perpendicular to 3x-2y+4z-5=0

  we get 3a-2b+4c=0 ------(3)

solve these three equations ..... you can get the values of a,b,c  

so you get the answer