Solve this following Question

Question:

A vector $\overrightarrow{\mathrm{n}}$ is inclined to $\mathrm{x}$-axis at $45^{\circ}$, to $\mathrm{y}$-axis at $60^{\circ}$ and at an acute angle to $\mathrm{z}$-axis. If $\overrightarrow{\mathrm{n}}$ is a normal to a plane passing through the point $(\sqrt{2},-1,1)$, then the equation of the plane is :

  1. $\sqrt{2} \mathrm{x}-\mathrm{y}-\mathrm{z}=2$

  2. $\sqrt{2} \mathrm{x}+\mathrm{y}+\mathrm{z}=2$

  3. $3 \sqrt{2} x-4 y-3 z=7$

  4. $4 \sqrt{2} \mathrm{x}+7 \mathrm{y}+\mathrm{z}=2$


Correct Option: , 2

Solution:

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