QUESION 18
Point on a Plane (coplanar) Choose one $\cdot 5$ points
Which point is on the plane with equation $2 z+3 y+2 z+2=0$
$\overrightarrow{T_{1}}=(1,0,2)$
$\vec{i}_{1}=(-3,0,2)$
$\vec{P}_{1}=(0,0,2)$

Step 1 ：We are given the equation of the plane as \(2z + 3y + 2z + 2 = 0\) and three points \((1, 0, 2)\), \((-3, 0, 2)\), and \((0, 0, 2)\).

Step 2 ：To find out if a point is on the plane, we can substitute the coordinates of the point into the equation of the plane. If the equation holds true, then the point is on the plane.

Step 3 ：Substituting the coordinates of the first point \((1, 0, 2)\) into the equation, we get \(2*2 + 3*0 + 2*2 + 2\), which does not equal to 0.

Step 4 ：Substituting the coordinates of the second point \((-3, 0, 2)\) into the equation, we get \(2*2 + 3*0 + 2*(-3) + 2\), which does not equal to 0.

Step 5 ：Substituting the coordinates of the third point \((0, 0, 2)\) into the equation, we get \(2*2 + 3*0 + 2*0 + 2\), which does not equal to 0.

Step 6 ：Since none of the equations hold true, none of the given points lie on the plane.

Step 7 ：Final Answer: \(\boxed{\text{None of the given points lie on the plane}}\).