Write the equation of the plane parallel to XOY-plane and passing through the point (2, -3, 5).

Explanation

Equation of `Y O Z` plane is `z=0`.


The required plane should pass through the point`(2,-3,5)`.


As known, the vector equation of a plane perpendicular to a given direction `(\vec{n})` and passing through a given point `(\vec{a})` is given by,


`(\vec{r}-\vec{a}) \cdot \vec{n}=0`


i.e. `[({x}-{x}_{1}) \hat{i}+({y}-{y}_{1} \hat{j})+({z}-{z}_{1}) \hat{k})] \cdot \hat{k}=0`


`\Rightarrow[({x}-(2)) \hat{i}+({y}-(-3)) \hat{j}+({z}-5) \hat{k}] \cdot \hat{k}=0`


`\rightarrow(z-5)=0`


We know, `\hat{i}=|\hat{i}||\hat{i}| \cos 0^{\circ}=1`,


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