Solve this following


A plane passing through the points $(0,-1,0)$

and $(0,0,1)$ and making an angle $\frac{\pi}{4}$ with the

plane $y-z+5=0$, also passes through the point

  1. $(-\sqrt{2}, 1,-4)$

  2. $(\sqrt{2}, 1,4)$

  3. $(\sqrt{2},-1,4)$

  4. $(-\sqrt{2},-1,-4)$

Correct Option: , 2


Let $a x+b y+c z=1$ be the equation of the plane

$\Rightarrow 0-b+0=1$

$\Rightarrow b=-1$


$\frac{1}{\sqrt{2}}=\frac{|0-1-1|}{\sqrt{\left(a^{2}+1+1\right)} \sqrt{0+1+1}}$

$\Rightarrow \mathrm{a}^{2}+2=4$

$\Rightarrow \mathrm{a}=\pm \sqrt{2}$

$\Rightarrow \pm \sqrt{2} \mathrm{x}-\mathrm{y}+\mathrm{z}=1$

Now for $-$ sign

$-\sqrt{2} \cdot \sqrt{2}-1+4=1$

option (2)

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