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三棱锥是一个特殊的棱锥:它的每个面皆可为棱锥的底面,每个顶点皆可为棱锥的顶点,而其体积总是不变的,利用这一点,我们可以把求点到面的距离转化成求三棱锥的高。这给求点到面、线到线的距离另辟了蹊径。一、求点到平面的距离求点到平面的距离,一般先作出过这点的平面的垂线,此点与垂足之间的部分即为所求。我们也可以把求点与面的距离转化成求三棱锥的高,进而利用等积的三棱锥来求。例1 正方体AC′的棱长为1,BC上有一点E,BE=1/3 BC,AA′上有一点F,AF=1/4 AA′,0为正方体的中心,求B′到面EFO的距离
A triangular pyramid is a special pyramid: each side of it can be the bottom of a pyramid, each vertex can be the vertex of a pyramid, and its volume is always the same. Using this, we can point to the point The distance translates into the height of the trigonal pyramid. This provides another measure for finding the distance from the surface to the line. First, find the distance from the point to the plane to find the distance from the plane, generally the first to make a vertical line of this point of the plane, the point between this point and the foot is the demand. We can also convert the distance from the point to the surface to find the height of the triangular pyramid, and then use the equal-area triangular pyramid to find it. Example 1 The square AC’ has an edge length of 1, BC has a point E, BE = 1/3 BC, AA′ has a point F, AF = 1/4 AA’, 0 is the center of the cube, seek B’ to the face EFO distance