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Question:

Given, point is (1, 2, 3)

and equation of plane is: x + y + z = 1

The normal vector of the plane is (1, 1, 1)

Now, the general equation of a plane is

      n * (x - x0 , y - y0 , z - z0 ) = 0          {n is the normal}

=> (1, 1, 1) *  (x - 1 , y - 2 , z - 3) = 0

=> x - 1 + y - 2 + z - 3 = 0

=> x + y + z - 6 = 0

=> x + y + z = 6

This is the required equation of the plane.

Answer:

Given, point is (1, 2, 3)

and equation of plane is: x + y + z = 1

The normal vector of the plane is (1, 1, 1)

Now, the general equation of a plane is

      n * (x - x0 , y - y0 , z - z0 ) = 0          {n is the normal}

=> (1, 1, 1) *  (x - 1 , y - 2 , z - 3) = 0

=> x - 1 + y - 2 + z - 3 = 0

=> x + y + z - 6 = 0

=> x + y + z = 6

This is the required equation of the plane.

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