What is the range of angles formed by a straight line on a different plane

The range of angles formed by heterogeneous lines is (0°, 90°).

At any point in space, two straight lines are parallel to two straight lines on different planes, and the acute angles (or right angles) formed by them are the angles formed by straight lines on different planes. The range of angles is (0°,90°]; The straight lines A and B are straight lines of different planes, and after passing through a point of space O, the lines A a, B B are drawn respectively, and the acute angles (or right angles) formed by intersecting lines A and B are called the angles formed by the straight lines A and B of different planes. , the angle formed by the straight line of the opposite plane is calculated as follows:

1) Translate one or both of them so that they intersect.

2) Connect the endpoints so that the corners are in a triangle. (or parallelograms, etc., in which the relationship between angles and angles can be easily found in the basic plane geometry).

3) Calculate the length of the three sides, and calculate the cosine value using the cosine theorem or sine theorem.

4) If the cosine value is negative, the opposite number is taken.

If it's zero, it's coplanar, it's actually parallel.

It's not intersecting, but it's not a straight line in the same plane.

If it's 0 degrees, it's not a straight line. Because if two straight lines are at an angle of 0 degrees, then they are parallel, and then they are coplanar straight lines.

0 degrees is coplanar, parallel to be precise.

If they are at an angle of 0 degrees, they are coplanar, then coplanarity contradicts "heteroplanar straight lines".

The range of angles formed by heterogeneous lines is (0°, 90°).

At any point in space, two straight lines are parallel to two straight lines on different planes, and the acute angle (or right angle) formed by them is the angle formed by the straight line of the opposite plane. The range of angles is (0°,90°]; The straight line A and B are straight lines of different planes, and after a point o in space, the lines A a, B B are drawn respectively, and the acute angles (or right angles) formed by intersecting lines A and B are called the angles formed by the straight lines A and B of different planes. , the angle formed by the straight line of the opposite plane is calculated as follows:

1) Translate one or both of them so that they intersect.

2) Connect the endpoints so that the corners are in a triangle. (or parallelograms, etc., in which the relationship between angles and angles can be easily found in the basic plane geometry).

3) Calculate the length of the three sides, and use the cosine theorem or sine theorem to calculate the cosine value.

4) If the cosine value is negative, the opposite number is taken.

Determination method:

1) Definition method: Judgment by definition that two straight lines can never be in the same plane, often used to disprove the method.

2) Decision theorem: the straight line that passes through the point outside the plane and the point inside the plane and the straight line that does not pass through the point in the plane are straight lines of different planes.

Example: Decision theorem: A line that intersects a plane and a line in the plane that does not pass through the intersection point are straight lines of different planes.

Known: ab = a, cd, a cd. Verification: AB and CD are straight lines on different planes.

Proof: Assuming that ab and cd are in the same plane, let this plane be . i.e. a, cd.

There are geometric and vector methods for finding the angles formed by heterogeneous straight lines.

1. Geometric method.

1.Translate one or both of the two lines into a plane.

2.Use corner relations to find (or construct) the triangle where the desired angle is located.

3.Find the proportional relationship of 3 or 3 sides, using cosine.

Theorem to find angles. 2. Vector method.

1.Find the direction vector of two straight lines.

2.Find the cosine of the angle between the two vectors.

3.Because the angle of the straight line is an acute angle, the cosine of 2 is taken as an absolute value.

This is the cosine value of the angle formed by the straight line.

An acute angle (or right angle) is an angle formed by a straight line on a different plane.

Two straight lines are parallel to two straight lines on different planes at any point in space, and the acute angle (or right angle) formed by it is the angle formed by the straight line on the opposite plane. The range of angles is (0°,90°];

Calculation of the angle formed by a straight line on a different surface:

1) Translate one or both of them so that they intersect.

2) Connect the endpoints so that the corners are in a triangle. (or parallelograms, etc., where the relationship between angles and angles can be easily found in hail and vertical basic plane geometry).

3) Calculate the length of the three sides, and calculate the cosine value using the cosine theorem or sine theorem.

4) If the cosine value is negative, the opposite number is taken.