The lines $L1$ and $L2$ have equations $r = 8i - 14j + 13k + s (-4i + 7j - 6k)$ and $x/2 = (y-17)/5 = (z+7)/-1$ respectively. The plane contains both $L1$ and $L2$:
a) Find the vector equation of the plane:
Obviously, the direction vectors of the plane are simply the direction vectors of the lines, although there are a number of different solutions to the direction vector I will be using these, that is $d1 = -4i + 7j - 6k$ and $d2 = 2i + 5j - k$.
So $x/2 = (y-17)/5 = (z+7)/-1$ is the equivalent of $r = (17j - 7k) + t (2i + 5j - k)$.
I am unsure how to find a point that I know the plane will pass through, it could be the interception of $L1$ and $L2$, but in that case by finding the intercept you get $s = 76/17$ and $t = 1/17$ as the solutions from comparing the $x$ and $y$ components, which when you plug back in gets a horrendous solution.
The textbook claims the answer is $(-4, 7, -5)$, but where do they get this point from?