How to calculate the straight-line distance on different planes is as follows:

The formula for the straight-line distance on different planes: d=|ab·n|/|n|. Assume that straight line n is a vector perpendicular to both opposite-surface straight lines a and b, a and b are any points on a and b respectively, and d is the distance between a and b, then d=|ab·n|/|n|.

1. Direct method: When the common vertical line segment can be made directly, find it directly. At this time, making and proving the common perpendicular segments of straight lines with different faces is the key to finding the distance of straight lines with different faces.

2. Conversion method: Convert line-to-line distance into line-to-surface distance. For example, to find the distance between straight lines a and b on different surfaces, first make a plane that passes through a and is parallel to b, then the distance between b and a It is the distance between a and b. Line-to-plane conversion method: It can also be converted into a plane that is parallel to a and a plane that is parallel to b. The distance between two parallel planes is the distance between two out-of-plane straight lines.

3. Volume bridge method: Use the line-surface distance and convert it into the height of the cone and use the volume formula to find it.

4. Constructor method: The principle of shortest distance is often used to construct a quadratic function, and the solution is solved by finding the optimal value of the quadratic function. The problem of the distance between two straight lines with different surfaces is not very demanding in the syllabus (the requirement is to calculate the distance when a common vertical line is given). Other solutions to this problem should be moderately exposed to broaden the mind.

Off-planar straight lines are two straight lines that are not on the same plane. Straight lines with different faces are straight lines that neither intersect nor are parallel. Because if two straight lines intersect or are parallel, they must be on the same plane. Unless otherwise specified, the straight lines in space refer to straight lines in different planes.

Properties of straight lines with different faces:

1. A straight line that intersects two straight lines with different faces at right angles is called the common perpendicular of two straight lines with different faces.

2. The line segment between the common perpendiculars of two different-planar straight lines is called the common perpendicular line segment of the two different-planar straight lines. The length of the common perpendicular line segment is called two The distance between straight lines on opposite sides.

3. A straight line passing through a point outside the plane and a point inside the plane, and a straight line in the plane not passing through the point are out-of-plane straight lines.

4. Through one of the two straight lines with different planes, there is a plane parallel to the other straight line.

5. The common perpendicular of straight lines with different planes exists and is unique.

6. Pick any point on each of the two straight lines with different faces. Among all the line segments formed by the two points, the distance between the two straight lines with different faces is the smallest.