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# Lecture - 6 Chapter 11 Three Dimensional Geometry

In this video, I am discussing equation of plane in three dimensional geometry and its derivation.

If One passing point and a normal vector is given then equation of plane in both the vector form and the Cartesian form:

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

\((x-x_1)a+(y-y_1)b+(z-z_1)c=0\)

If three non-collinear point are given then equation of plane in both the vector form and the Cartesian form:

\((\vec{r}-\vec{a})\cdot[(\vec{b}-\vec{a})\times(\vec{c}-\vec{a})]=0\)

\(\left|\begin{matrix}x-x_1&y-y_1&z-z_1\\x_2-x_1&y_2-y_1&z_2-z_1\\x_3-x_1&y_3-y_1&z_3-z_1\\\end{matrix}\right|=0\)

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