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一、知识要点 1.已知非零向量a,如何求其方向上的单位向量? 设a方向上的单位向量为e,则a=|a|e, ∴e=a/|a|,于是有命题非零向量a方向上的单位向量等于a/|a|,其反方向上的单位向量等于-a/|a|。 2.求含坐标的单位向量,有两种方法,一种是1中的方法,另一种是解方程组。 3.单位向量与角。 (1)二面角的大小,可用两半平面的法单位向量的夹角求之,即二面角的度数与两半平面的法单位向量的夹角相等或互补。
First, the knowledge points 1. Known non-zero vector a, how to find the direction of the unit vector? Let a direction of the unit vector e, then a = | a | e, ∴e = a / | a |, so There is a proposition that the unit vector in the non-zero vector a direction is equal to a/|a|, and the unit vector in the reverse direction is equal to -a/|a|. 2. There are two methods for finding the unit vector containing coordinates. One is the method in 1 and the other is the solution of the equations. 3. Unit vector and angle. (1) The size of the dihedral angle can be determined by the angle between the unit vectors of the two half-planes, that is, the angle between the dihedral angle and the unit vector of the two half planes is equal or complementary.