Point of Intersection of Three Planes Calculator

An online calculator to calculate the coordinates of the point of intersection of three planes in 3D is presented.

Solve System of Equations to Find the Point of Intersection

The equation of each plane is of the form
\[ a x + b y + c z = d \]
Given the equations of three planes,
\( \quad a_1 x + b_1 y + c_1 z = d_1 \)   ,   \( a_2 x + b_2 y + c_2 z = d_2 \)   and   \( a_3 x + b_3 y + c_3 z = d_3 \),
the coordinates \( (x,y,z) \) of point of intersection of the three planes given by the three equations above, is found by solving the 3 by 3 system of equation given by
\[ \begin{array}{lcl} a_1 x + b_1 y + c_1 z & = & d_1 \\ a_2 x + b_2 y + c_2 z & = & d_2 \\ a_3 x + b_3 y + c_3 z & = & d_3 \end{array} \] An example is shown in the graph below.
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Use of Calculator

Enter the twelve coefficients describing the three planes and press "Calculate Intersection".