Answer :

The equation of a plane passing through (x1,y1,z1) and perpendicular to a line with direction ratios A, B, C is

A(x - x1) + B(y - y1) + C(z - z1) = 0


The plane passes through (a,b,c)


So, x1 = a, y1 = b, z1 = c


Since both planes are parallel to each other, their normal will be parallel


Direction ratios of normal


= Direction ratios of normal of


Direction ratios of normal = (1,1,1)


A = 1, B =1, C = 1


Thus,


Equation of plane in cartesian form is


A(x - x1) + B(y - y1) + C(z - z1) = 0


1(x - a) + 1(y - b) + 1(z - c) = 0


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


Thus, x + y + z = a + b + c is the required equation of plane.


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