Determine the equation of the plane that goes through 2 given points, and which forms a given angle with another plane

Question

I hope someone can help me with this one too.

Determine the equation of the plane which goes through the points $M(0,2,0)$ and $N(2,0,0)$, and which forms an angle of $\pi/3$ with the plane $x=0$.

Answer 1

Hint 1: start withvthe equation of the plane in the form $$ax+by+cz=d$$

Since $M$ and $N$ lie on the plane, you can obtain the equation of the plane with just one unknown coefficient.

Hint 2: the planes are at angle $\frac{\pi}{3}$ means their normals are also, so you can use dot product to determine the values of this unknown coefficient.