So I have this maths question that I can't seem to wrap my head around. I have two lines:
Line 1 $= r = 3i+2j+7k + X(i-j+3)$
Line 2 $= r = 6i+5j+2k + Y(2i+j-k)$
I have found the point of intersection when $X=-1$ and $Y=-2$, and thus the point of intersection to be $2i+3j+4k$
Now I have been told that a vector $(i+aj+bk)$ is perpendicular to both, and to find $a$ and $b$. I understand how this is, but can't seem to find the answer. I can't use dot product with two unknowns, so I would really appreciate some help.
P.S I'm not sure how you're properly supposed to structure these questions with the fancy format so if anyone could link me to how I am supposed to lay questions out please do.