Stereo geometry is a mandatory mathematics test for college entrance examination. Many students will not draw on the auxiliary line and the coordinate system will not be built. This material makes a template of the steps of establishing the spatial vector, calculating the normal vector, and finding the dihedral angle, and you can get points according to the step set, which is suitable for the end of the sprint.
The three-dimensional geometry questions account for 12-15 points in the college entrance examination, which belongs to the question type of “there are templates to follow”. Master the routine of space vectors, this kind of problem is to send sub-questions; without mastery, it is a “roadblock” that can not be done.
1. Why use space vectors?
Traditional geometry needs to draw auxiliary lines, find vertical relationships, and rely on spatial imagination. Spatial vectors turn geometric problems into algebraic problems. As long as they can build systems and calculate, they can score points mechanically. Especially friendly to classmates who don’t have a strong sense of space.
2. Establishing a system is the first step and the most critical step
The system was built, and the back was all smooth; the system was built wrong, and all of them lost. Remember the mantra: there are right angles with right angles, no right angles to find the midpoint. Straight prisms, rectangles, and square pyramids all have natural right angles and are built directly; generally, the triangular pyramid first finds the high line and then builds the system.
3. Normal vector method should be proficient
The normalization vector is the core operation of the stereo geometric space vector problem: set n = (x, y, z), column two equations (n · a = 0, n · b = 0), and solve the equation system. It can be found within 30 seconds after proficiency. Note that the results should be reduced to their simplest form.
IV. Formula Memory Secrets
The linear angle looks at the “sinusoidal value of the angle between the normal vector and the directional vector”; the dihedral angle looks at the “cosine value of the angle between the two normal vectors” (pay attention to whether the acute angle or the obtuse angle is taken); the distance of the point surface is “vector projection method”. Ripen the three formulas and get at least 10 points for the big questions.
This full version of Word recommends printing, pasting the four-step template on the notebook, and checking it against the question each time.
Tip: The webpage is in preview. Click the green button above to download the full version of Word, which can be printed and edited.
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