Question

Find the equation of the place through (1,2,3) and parallel to the plane 3x+4y -5z = 0 ​

Answer 1

Solution:- let the point (1,2,3) is passing through the plane a(x-1) + b(y-2) + c(z-3)

plane (1) is parallel to the given place 3x+4y -5z = 0

a/3= b/4 = c/-5 = k {Let}

a = 3K , b = 4k , c = -5K

put value of a, b, and c in equation (1)

a(x-1) +b(y-2) + c(z-3) = 0

K [ 3x-3+4y-8-5z+15] = 0

•°• 3x + 4y -5z+4 = 0 Answer

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Answer 2

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Solution:- let the point (1,2,3) is passing through the plane a(x-1) + b(y-2) + c(z-3)

plane (1) is parallel to the given place 3x+4y -5z = 0

a/3= b/4 = c/-5 = k {Let}

a = 3K , b = 4k , c = -5K

put value of a, b, and c in equation (1)

a(x-1) +b(y-2) + c(z-3) = 0

K [ 3x-3+4y-8-5z+15] = 0

•°• 3x + 4y -5z+4 = 0 ( proved)