难点3 运用向量法解题（Difficulty 3 using vector method to solve problems）Difficulty 3 using vector method to solve problemsThe plane vector is one of the new reform of teaching content, the use of new materials in recent years, the college entrance examination gradually increased to this part of the test strength, this section is mainly to help the candidates to analysis by vector method, to solve the related problems.Difficult magnetic field(* assumes) triangle ABC, A (5, 1), B (1, 7), C (1, 2), and (1) BC on the side of the midlineAM long; (2) the bisector AD long angle CAB; (3) the value of cosABC.Case studyA case of Figure 1, known parallelepiped ABCD - A1B1C1D1 ABCD is shown at the bottom of the diamond, and / C1CB= / C1CD= / BCD.(1): C1C group BD. confirmation(2) when the EMBED Equation.3 value is how much they can make A1C an C1BD plane? Please give me proofPropositional intention: this topic mainly examines the examinee, uses the vector method to solve the vector vertical, the angle and so on, as well as to the three-dimensional geometry graph reading abilityKnowledge support: the shining point of answering the question is to demonstrate the vertical problem of solid geometry by vectors, which makes the geometry problem algebraic and makes the tedious argument easyThe error analysis: difficulty is not clear and the mutual transformation test physiological positional relationship and the relationship between the number of topics, and then is to clarify the difference and contact angle and the vector angle provided by known conditions.Techniques and methods: using a B EMBED Equation.3 a, an b=0 to prove the two straight vertical, as long as the number that corresponds to the two linear vector product is zero.(1) prove that if EMBED Equation.3 =a, EMBED Equation.3 =b, EMBED Equation.3 =c, according to the meaning of problems, |a|=|b|, 22 EMBED Equation.3, EMBED Equation.3, EMBED Equation.3 in La angle theta, so EMBED Equation.3 =a B, EMBED Equation.3 =c (a b) - =c - b=|c| - |a|cos - |c| Ac |b|cos 0 =0 BD. C1C * t(2): if the solution of anomalous A1C plane C1BD, A1C an BD card only, A1C group of DC1,By EMBED Equation.3= (a+b+c) - (Ac) =|a|2+a - Bb - C|c|2=|a|2|c|2+|b| - |a|cos - |c| - cos |b| theta theta =0, tooWhen |a|=|c|, an A1C DC1, in the same way as the |a|=|c|, A1C group of BD,EMBED Equation.3 * =1, A1C an C1BD. planeA case of 2 figure, straight three prism ABC - A1B1C1, CA=CB=1 ABC, a bottom surface, angle BCA=90 degrees, AA1=2, M, N, A1B1, A1A respectively is the midpoint.(1) seek the length of EMBED Equation.3;(2) the value of cos;(3): A1B group C1M. confirmationPropositional intention: this topic mainly examines the examinee uses the coordinate method in the vector method to solve the solid geometry questionAssumes the title level.Knowledge support: the shining point of answering the question is to establish the proper space rectangular coordinate system O - XYZ, and then find the coordinates of the points and find the coordinates of the vectorsThis is the difficulty of analysis are: the construction of system, the candidates can not find the point of correct coordinates.Techniques and methods: you can find the coordinates of the A, B and C points in the plane coordinate surface xOy, and then use the modulus and direction of the vector to find the coordinates of the other points(1) solution: as shown in this paper, the space Cartesian coordinate system O - xyz. is established with C as the originAccording to the meaning of problems: B (0, 1, 0), N (1, 0, 1)EMBED Equation.3 EMBED Equation.3 * | |=.(2): A1: according to the solution of (1, 0, 2), C (0, 0, 0), B1 (0, 1, 2).Equation.3 = Equation.3 = EMBED * EMBED (0, 1, 2)EMBED Equation.3 =1 * 0+ * 1+2 * 2=3 (1)EMBED Equation.3 EMBED Equation.3 |= |EMBED Equation.3EMBED Equation.3Proof: (3) according to the meaning of problems: C1 (0, 0, 2), M (EMBED Equation.3)EMBED Equation.3* EMBED Equation.3A1B C1M. * t- one1. solve on the vector problem, a good use of vector translation, scaling, synthesis, decomposition and transformation, correctly calculates vectors, deepen our understanding of the nature of the vector. Two vector coordinate operation reflects the number and shape each other and closely combined with the transformation of thought.Dot product of 2. vectors is often used in the vector is equal to two, and the angle of vertical vector projective problems. Coordinate calculation used to prove the vector vector perpendicular and parallel; the distance angle by using vector angle formula and the distance formula of two lines and the space between two points.ThreeSpace vector can be used to solve the problem of solid geometry:(1) what vector knowledge can be used to solve the problem? What vectors do you need to use?(2) whether the required vector