• # question_answer A plane passing through the points (0, -1, 0) and (0, 0, 1) and making an angle $\frac{\pi }{4}$with the plane $yz+5=0,$also passes through the point             [JEE Main 9-4-2019 Morning] A) $\left( -\sqrt{2},1,-4 \right)$               B) $\left( \sqrt{2},1,4 \right)$C) $\left( \sqrt{2},-1,4 \right)$                 D) $\left( -\sqrt{2},-1,-4 \right)$

Let $ax+by+cz=1$be the equation of the plane $\Rightarrow 0-b+0=1$$\Rightarrow b=-1$ $0+0+c=1$$\Rightarrow c=1$ $\cos \theta =\left| \frac{\vec{a}.\vec{b}}{\left| {\vec{a}} \right|\left| {\vec{b}} \right|} \right|$ $\frac{1}{\sqrt{2}}=\frac{\left| 0-1-1 \right|}{\sqrt{\left( {{a}^{2}}+1+1 \right)}\sqrt{0+1+1}}$ $\Rightarrow {{a}^{2}}+2=4$$\Rightarrow a=\pm \sqrt{2}$$\Rightarrow \pm \sqrt{2}x-y+z=1$ Now for -sign $-\sqrt{2}.\sqrt{2}-1+4=1$ option [b]