Three Dimensional Geometry Part 2

First line is (ϕ+α,2ϕ+1,3ϕ+1)
and second line is (qβ+4,3q+6,3q+7).
For intersection
ϕ+α=qβ+4 .....(i)
2ϕ+1=3q+6 ......(ii)
3ϕ+1=3q+7........(iii)
for (ii) & (iii) ϕ=1,q=−1
So, from (i) α+β=3
Now, point of intersection is (α+1,3,4)
It lies on the plane.
Hence, α=5&β=−2