The straight line $a$ lies in the plane $\alpha$ , the straight line $b$ intersects $\alpha$ in point $M$. If $M$ doesn't belong to the $a$ prove that there isn't plane which contains the two straight lines.
I don't have idea how to prove this, I thought about proving that the two lines have six dots, that aren't the same but firstly I don't have any idea how to do that and secondly, even if I prove this I will just prove that there are two planes which contain both lines and aren't the same one plane.
Say a plane $\beta$ contained both $a$ and $b$. $\beta$ would contain both $a$ and $M$. But $M \not\in a$, so $\beta$ must coincide with $\alpha$. (There is a unique plane through any given line and point not on it.) Since $\alpha$ does not contain $b$, we have a contradiction.