The given lines are represented by the equations:
(Line 1) and (Line 2).
To check if the lines are coplanar, we can use the condition that the determinant formed by the direction vectors of the lines and the vector connecting a point from each line must be zero. Let us consider the points on Line 1 and on Line 2.
The direction vector of Line 1 is and for Line 2, . The vector connecting the point from Line 1 to the point on Line 2 is .
For coplanarity, the determinant of the matrix formed by these vectors must be zero:
Expanding this determinant, we have:
Solving, we get:
Which simplifies to:
Simplify further:
Now, solve the quadratic equation:
Using the quadratic formula, :
After calculations, we seek additional values by factoring or testing the given options. Upon testing, we find solutions that match:
For potential integer roots when expanded and solved normally, the values that satisfy the condition are:
or