Q23 of 45 Page 1

Find the equation of the plane determined by the points A(3, –1, 2), B(5, 2, 4) and C(–1, –1, 6) and hence find the distance between the plane and the point P(6, 5, 9).

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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