# Find the eq

Given that, a plane is passes through the point (3, 2, 0) so equation will be

a(x – 3) + b(y – 2) + c(z – 0) = 0

a(x – 3) + b(y – 2) + cz = 0 ……(1)

plane also contains the line

so it pass through the point (3, 2, 0)

a(3 – 3) + b(6 – 2) + c(4) = 0

4b + 4c = 0 …… (2)

Also plane will be parallel to,

a(1) + b(5) + c(4) = 0

a + 5b + 4c = 0 ……(3)

solving (2) and (3) by cross multiplication,

a = – k, b = k, c = – k

put a = – k, b = k, c = – k in equation (i) we get

(– k)(x – 3) + (k)(y – 2) + (– k)z = 0

– x + 3 + y – 2 – z = 0

x – y + z – 1 = 0

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