Answer:

Explanation:
Equations of lines,
x + y - z = 2,
2x - y + 3z = 2
If z = 0,
Equations would be,
x + y = 2
2x - y = 2
Adding these equations, we get, 3x = 4 ⇒ x =


Thus, solution would be ( 4/3, 2/3, 0)
Now, if x = 0,
Equation are,
y - z = 2,
-y + 3z = 2
Adding equations, We get, 2z = 4 ⇒ z = 2,
⇒ y - 2 = 2 ⇒ y = 2 + 2 = 4,
Thus, solution would be ( 0, 4, 2 )
Let a be the vector from (-2, 2, 3) to (4/3, 2/3, 0)
⇒ a = (4/3 + 2)i + (2/3 -2)j + (0-3)k =

Similarly,
Let b be the vector from (-2, 2, 3) to (0, 4, 2),
⇒ b = (0+2)i + (4-2)j + (2-3)k ⇒ b = 2i + 2j - k
So, the normal of the plane is,

∵ General equation of a plane,

Hence, the equation of the given plane is,




