# Find the equation

Given; the points A(3, –1, 2), B(5, 2, 4) and C(–1, –1, 6)

Substituting these equations in the equation for planes:

3p − q + 2r = 1 …… (i)

5p + 2q + 4r = 1 …… (ii)

−p − q + 6r = 1 …… (iii)

(i) − (iii)

4p − 4r = 0

p = r

Substituting this in (ii)

9p + 2q = 1 ……(iv)

Substituting this in (i)

5p − q = 1 ……(v)

(iv) + 2 (v)

19p = 3

Equation of the plane is:

3x − 4y + 3z = 19 is the required equation.

Distance from (6,5,9) to above plane is:

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