Question

Find the equation of the planes passing through points $(1,0,0)$ and $(0,1,0)$ and making an angle of $0.25\pi$ radians with the plane $x+y-3=0$.

Answer 1

$ax+by+cz=d$ $a=d$

$b=d$

$ax+ay+cz=d$

$a+a=\sqrt{a^2+a^2+c^2}\sqrt{1+1}\frac{1}{\sqrt{2}}$

$2\sqrt{2}a=\sqrt{a^2+a^2+c^2}\times \sqrt{2}$

$4a^2=2a^2+c^2$ $ax+ay\pm \sqrt{2}a=9$

$2a^2=c^2$ $x+y\pm \sqrt{2}z=1$

$\sqrt{2}a=c$

$c=\sqrt{2}a$