Question

Find the equation of the plane passing through (a, b, c) and parallel to the plane r.(i + j + k) = 2.

Answer 1

Answer:

x+y+z-a-b-c=0

is the required equation of the plane

Step-by-step explanation:

To find the equation of the plane passing through (a, b, c) and parallel to the plane r.(i + j + k) = 2.

first convert the given plane in cartesian form

Let

$\vec r= x\hat i+y\hat j+z\hat k\\\\(x\hat i+y\hat j+z\hat k).(\hat i+\hat j+\hat k)=2\\\\x+y+z-2=0$---eq1

Now the plane whose equation we had to find is parallel to the plane in eq1

So equation of plane is x+y+z+λ=0 for some constant λ---eq2

Now the plane passes through (a,b,c) point,means it satisfies the equation of the plane

a+b+c+λ=0

λ=-a-b-c

Now put the value of λ  in the eq2

x+y+z-a-b-c=0

is the required equation of the plane.