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How to find the tangent value of dihedral angle in solid geometry by using space vector in college entrance examination mathematics problems
Answer: 1. If the normal vectors of these two planes are known, divide the dot product of the normal vectors of these two planes by the product of the modules of these two normal vectors; Find the cosine of two normal vectors. This cosine is the negative cosine of two plane angles; If the plane angle is a, the cosine value is cos( 180D-a)=-cosa. Sina = √ (1-cos 2a) (positive number-arithmetic root); Tangent value: tana=sina/-cosa.

2. Find any two sides of each plane of two planes without knowing the normal vector of the plane (as long as the two sides in the same plane are not perpendicular to each other); As the vector of each side, the cross product of two vectors in the same plane is the normal vector of this plane (note that if you can't judge whether two angles are acute or obtuse, press the right hand system to make the normal vector point to the inner direction of the plane angle); Then find the cosine of two normal vectors; Others are the same as 1.