![]() \overrightarrow N = 0 \) Equation of a Plane Passing Through Three Non Collinear Points \((\overrightarrow r - \overrightarrow a). Solving this further we have the following expression. \(\overrightarrow AP.\overrightarrow N = 0\). Here we have the dot product of these two lines equal to zero. The line \(\overrightarrow AP \) lies in this referred plane and is perpendicular to the normal \(\overrightarrow N\). Let us consider another point P in the plane having a position vector \(\overrightarrow r \). Let us consider a point A in the plane with a position vector \(\overrightarrow a\), and a vector \(\overrightarrow N\), which is perpendicular to this plane. \(\overrightarrow r.\hat n = d \) Equation of a Plane Perpendicular to a given vector and through a Point Finally, we have the following expression for the dot product of these two lines as follows. Also \(\overrightarrow NP\) and \(\overrightarrow ON\) are perpendicular to each other, and the dot product of these two perpendicular lines is equal to 0. We now have \(\overrightarrow NP = \overrightarrow r - d. Further, we shall consider a point P in the plane, having a position vector of \(\overrightarrow r\). Let the length of the normal \(\overrightarrow ON\) be d units, such that \(\overrightarrow ON = d \hat n\). Normal is a perpendicular line drawn from the origin O to a point N in the plane, such that \(\overrightarrow ON \) is perpendicular to the pane. Let us consider a normal \(\overrightarrow ON \) to the plane. Here we shall aim at understanding the proof of different methods to find the equation of plane. ![]() The equation of a plane passing through the intersection of two planes \(\overrightarrow r.The equation of a plane passing through three non collinear points \(\overrightarrow a\), \(\overrightarrow b\), and \(\overrightarrow c\), is \((\overrightarrow r - \overrightarrow a) = 0\).The equation of a plane perpendicular to a given vector \(\overrightarrow N \), and passing through a point \(\overrightarrow a\) is \((\overrightarrow r - \overrightarrow a).Equation of a plane at a perpendicular distance d from the origin and having a unit normal vector \(\hat n \) is \(\overrightarrow r.The following are the four different expressions for the equation of plane. The equation of a plane can be computed through different methods based on the available inputs values about the plane.
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