1. Distance from point to plane: let vector P be the normal vector of plane M, list equations, and solve A P. Let point B be the intersection of straight lines passing through point A and perpendicular to m. According to A and vector P, the coordinates of B can be obtained, and the distance between ab is the distance from point to straight line. In addition, the formula can be directly used: the distance from point A (x0, y0, z0) to plane x+By+Cz+D=0 is equal to the absolute value of Ax0+By0+Cz0+D divided by the square root of A 2+B 2+C 2.
2. Distance from a straight line to a parallel plane: the common perpendicular of the straight line and the parallel plane is equal, so you can take any point on the straight line and solve it according to the distance from the point to the plane.
3. Distance between parallel planes: The common vertical lines between parallel planes are equal, so you can take any point on one of the planes and solve it according to the distance from the point to the plane. In addition, the formula can be directly used: the distance between plane Ax+By+Cz+D 1=0 and plane Ax+By+Cz+D2=0 (the two planes are parallel, and the parameters A, B and C can be adjusted to be the same) is the absolute value of D 1-D2 divided by the absolute value of A 2+B 2+C 2.
4. Distance of straight lines on different planes: First, we can find out the problem that a straight line passes through the parallel plane of another straight line and is converted into a straight line to a parallel plane, but this is more troublesome. The second is to find the common normal vector p of two straight lines, and then take any point on each of the two straight lines to get a vector. The projection of this vector on p is the distance between straight lines in different planes, and the formula is more troublesome ... see figure.
By the way, aren't there any formulas in your textbooks? -