### Vector Equation of the Plane

To determine the equation of a plane in 3D space, a point P and a pair of vectors which form a basis (linearly independent vectors) must be known. The point P belongs to the plane π if the vector is coplanar with the vectors and .   ### Parametric Equations of the Plane  ### Cartesian Equation of the Plane

A point is in the plane π if the system has the solution:   The values are given as:    ### Intercept Form A(a, 0, 0), B(0, b, 0) and C(0, 0, c).  ### Examples

1.Find the equations of the plane that pass through point A = (1, 1, 1) and their direction vectors are: and .   2.Find the equations of the plane that pass through points A = (−1, 2, 3) and B = (3, 1, 4) and contains the vector .   3.Find the equations of the plane that pass through points A = (−1, 1, −1), B = (0, 1, 1) and C = (4, −3, 2).    4. π is the plane of parametric equations: Confirm whether the points A = (2, 1, 9/2) and B = (0, 9, −1) belong to this plane.   5.Find the equation of the plane in intercept form that passes through the points A = (1, 1, 0), B = (1, 0, 1) and C = (0, 1, 1).   Divide by −2, and the equation is obtained: 6.Find the equation of the plane that passes through the point A = (2, 0, 1) and contains the line with the equation: From the equation of the line, a second point and the vector is obtained.   7.Find the equation of the plane that passes through the points A = (1, −2, 4) and B = (0, 3, 2) and is parallel to the line:   8.Given the lines: Determine the equation of the plane that contains the line r and is parallel to the line s.  Did you like the article?     (1 votes, average: 5.00 out of 5) Loading...

Emma

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