The vector $A=3 i + j - k$ is normal to the plane $M_1$, and the vector $B=2i - j + k$ is normal to a second plane $M_2$. Do the two planes necessarily intersect if they are both extended indefinitely?
Justify answer and also validate the answer.
My thoughts on this is to use dot product and cross product, where the lines will meet but it can be showed that it is not parallel to each other.
Hint: M1 has equation $3x+y-z=a$ for some $a$.Likewise, M2 has equation $2x-y+z=b$. All you have to do is to show the system of these two equations has a solution.