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Notes
\(\text{Equation of a Plane Given 3 Points}\)
\( \left| {\begin{array}{ccc}x-x_1 & y-y_1 & z-z_1 \\x_2-x_1 & y_2-y_1 & z_2-z_1 \\x_3-x_1 & y_3-y_1 & z_3-z_1 \\\end{array} } \right|=0\)
Practice Problems
Find the equation of the plane through the following points.
\(\textbf{1)}\) \((1,2,3), (4,2,6), (-2,8,9)\)
\(\textbf{2)}\) \((5,3,2), (7,7,7), (-1,0,5)\)
\(\textbf{3)}\) \((2,2,2), (4,-1,-1), (0,0,1)\)
\(\textbf{4)}\) \((0,0,0), (1,1,1), (7,8,9)\)
\(\textbf{5)}\) \((1,2,3), (1,4,6), (1,8,-3)\)
See Related Pages\(\)
\(\bullet\text{ Displacement Vectors}\)
\(\,\,\,\,\,\,\,\,(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}…\)
\(\bullet\text{ Magnitude, Direction, and Unit Vectors}\)
\(\,\,\,\,\,\,\,\,|\vec{u}|=\sqrt{a^2+b^2}…\)
\(\bullet\text{ Dot Product}\)
\(\,\,\,\,\,\,\,\,a \cdot b=x_1 x_2+ y_1 y_2…\)
\(\bullet\text{ Parallel and Perpendicular Vectors}\)
\(\,\,\,\,\,\,\,\,⟨8,2⟩ \text{ and } ⟨−4,−1⟩…\)
\(\bullet\text{ Scalar and Vector Projections}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{a \cdot b}{|b|^2} \, \vec{b}…\)
\(\bullet\text{ Cross Product}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Equation of a Plane}\)
\(\,\,\,\,\,\,\,\,Ax+By+Cz=D…\)
\(\bullet\text{ Andymath Homepage}\)
In Summary
An equation of a plane is a mathematical representation of a flat surface that extends indefinitely in all directions. A plane can be defined by 3 non-collinear points.
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