How to find the cosine of the angle between two vectors!

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• 1. As shown in the figure, ab ∥ CD, ∠ ACB = 90 °, e is the midpoint of AB, CE = CD, de and AC intersect at point F
• 2. What is the multiplication of two vectors with equal modules and opposite directions
• 3. As shown in the figure, in the triangle ABC, high AD and be intersect at h, AC = BH
• 4. Given the vector a = (- 1,1), B = (4,3), how to find their scalar product?
• 5. The triangle is a trigonometric arithmetic sequence with the circumference of 36 and the circumference of the inscribed circle of 6 π Calculate a side length of 12, inscribed circle radius of 3, then how to do
• 6. Let a > 0, b > O, prove: ln (a + b) / 2 > = (LNA + LNB) / 2
• 7. A cylinder billet with a bottom radius of 4cm and a height of 5cm is melted into a cone with a bottom diameter of 20cm. What is the height of the cone?
• 8. Given the set M = {y ∈ r y = x & # 178;}, n = {y ∈ R x & # 178; + Y & # 178; = 4}, then m ∩ n = a {[- 1,1}, [1] Given the set M = {y ∈ R, y = x & # 178;}, n = {y ∈ R, X & # 178; + Y & # 178; = 4}, then m ∩ n = 1 A{【﹣1,1},【1,1】} B{1} C{x ﹣2≤x≤2} D{x 0≤x≤2} Given that a = {1,3}, B = {x [x-4] [x-a] = 0}, if the sum of all elements in a ∪ B is 8, then the set of a is Let x = 3-5 times 1 / 6 of radical, y = 3 + radical 6 π, z = 2 under radical 3 + 2 under radical 3 + radical 3, set M = {m m = a + B radical 6, a ∈ Q, B ∈ Q} then the relation between X, y, Z and set M is
• 9. It is known that in square ABCD, e is the point above AB, passing through e as EF ⊥ AB, intersecting BD with F, and G is the midpoint of DF, connecting eg and CG
• 10. Find the indefinite integral of X / (x ^ 3 + 8)
• 11. As shown in the figure, △ ABC, D and E are the midpoint of BC and AC respectively. BF bisects ∠ ABC and intersects de at point F. if BC = 6, the length of DF is______ ．
• 12. It is known that a is the unit vector in the plane. If B satisfies b * (a-b) = 0, then the value range of the module of B is? Why not - 1 ≤| B | ≤ 1
• 13. A circle is an axisymmetric figure. There are countless axes of symmetry, and its axis of symmetry is the diameter of the circle?
• 14. Pentagram is an axisymmetric figure. How many axes does it have?
• 15. One yuan equation application problem (sixth grade) SOS! It's 30 kilometers per hour from home to the railway station, 15 minutes earlier than the train's departure time. If it's 18 kilometers per hour, it's 15 minutes later than the train's departure time?
• 16. On a 1:500 scale plan, the perimeter of a rectangular classroom is 10cm, and the ratio of length to width is 3:2 Find the ratio of the area on the picture to the actual area of the classroom Write the ratio of area to time area on the graph and compare it with the scale. What do you find?
• 17. Eighth grade mathematics volume I mid-term test questions which have
• 18. The story of curved moon, stars and round moon
• 19. Using vector to solve four centers of triangle Note: generally, capital letters represent vectors, and vector * vector represents the product of two vectors 1. Prove that point O is the center of gravity of triangle ABC, which is AOB = BOC = COA 2. Prove: if h is a point in the plane of triangle ABC, and the square of the module of HA + the square of the module of BC = the square of the module of HB + the square of the module of Ca = the square of the module of HC + the square of the module of ab, then h is the perpendicular center of triangle ABC 3. Prove: if OA * (module of AB / AB - module of AC / AC) = ob * (module of Ba / BA - module of BC / BC) = OCT (module of Ca / Ca - module of CB / CB) = 0, then o is the inner core of triangle ABC 4. Prove that point O is a certain point on the plane, A.B.C is three non collinear points on the plane, the moving point P satisfies OP = OA + m (cosine value of the module and angle B of AB / AB + cosine value of the module and angle c of AC / AC), and M is greater than 0, then the trajectory of point P must pass the perpendicular center of triangle ABC
• 20. The bottom of a right angled trapezoid is 1.5 times of the top, and the top is extended by 16 cm to become a square. The area of the right angled trapezoid is calculated Elementary school mathematics, not equations