Please help me with this task!
Thanks in advance!
You can equate x's, y's and z's and get three equations and three variables. Note that the value of t of the two lines don't have to be the same at the intersection point.
The vector (2, 1, 4) lies in the first line, and (a, -2, 1) lies in the second line. Once you know the intersection point and two vectors in the plane, you can use these methods to construct the plane equation.
When working with lines always use different parameters.
$\displaystyle \left\{ {\begin{array}{l} {x = 1 + 2t} \\ {y = 7 + t} \\ {z = 3 + 4t} \\\end{array}} \right.\;\& \,\left\{ {\begin{array}{l} {x = 6 + as} \\ {y = - 1 - 2s} \\ {z = - 2 + s} \\\end{array}} \right.$
Now solve the second two.
Then find the value of $\displaystyle a.$