"Plane equation" refers to the equation corresponding to all points on the same plane in space, and its general form is Ax+By+Cz+D=0.
The cross product can be used as the normal of the three-point plane.
The graph of any ternary linear equation is always a plane, where the coefficients of x, y, z, y and z are the coordinates of a normal vector of the plane.
Two mutually perpendicular planes are equivalent to a1a2+b1B2+c1C2 = 0.
Parallelism or coincidence of two planes is equivalent to a1/a2 = b1/B2 = c1/C2.
Distance from point to plane = ABS (AX0+BY0+CZ0+D)/SQRT (A 2+B 2+C 2) Solution process: the mapping Prj (small n) of a straight line connecting two points inside and outside the plane on the normal vector (with arrow p 1p 0 = product of quantity.
Extended data:
Let the plane equation be Ax+By+Cz+D=0. If d is not equal to 0, take A =-D/A, B =-D/B and C =-D/C, then we can get the intercept equation of the plane: x/a+y/b+z/c= 1?
Its intersections with the three axes are p (a, 0, 0), q (0, b, 0) and r (0, 0, c), where a, b and c are called the intercept of the plane on the x, y, z, y and z axes in turn.
Nature:
① A row (or a column) in determinant A is multiplied by the same number k, and the result is equal to kA.
② determinant a is equal to its transposed determinant at (the I-th row of at is the I-th column of a).
③ If there is a row (or a column) in the determinant of order n |αij|; The determinant |αij| is the sum of two determinants, where the first row (or column) is B 1, B2, ..., bn; The other is с 1, с 2, …, с n; The elements in other rows (or columns) are exactly the same as those in |αij|.
④ Two rows (or columns) in determinant A are interchanged, and the result is equal to -a..⑤ Multiply each element in one row (or column) of determinant A by a number, and then add it to each corresponding element in another row (or column), and the result is still A. ..
References:
Baidu Encyclopedia-Plane Equation