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In the cube abcd-a1b1c1d1, M is the midpoint of Aa1 ditto
Let the side length be 2, take the midpoint n of BD, connect MD and C1d, then it is easy to prove that Mn is vertical to BD, c1n is vertical to BD, so the angle mnc1 is the plane angle of dihedral angle m-bd-c1. The square of MC1 = the square of A1C + the square of a1m = 8 + 1 = the square of 9mn = the square of Ma + the square of an = 1 + 2 = 3nc1 = the square of CC1 + the square of c1n = 4 + 2 = 6
In the cube abcd-a1b1c1d1 with edge length a, M is the midpoint of Aa1, then the distance from point A1 to plane MBD is ()
A. 63aB. 36aC. 34aD. 66a
The distance from a to plane MBD can be obtained by isoproduct deformation. Va-mbd = vb-amd, that is: 112a3 = 13 × D × 12 × 2A × & nbsp; 54a2 − 24a2, that is, it is easy to find d = 66A
In the cube abcd-a1b1c1d1, M is the midpoint of Aa1
High school sophomore?
In the square abcd-a1b1c1d1, M is the midpoint of Aa1, and it is proved that the plane MBD is perpendicular to the plane bdc1
It is proved that: take the midpoint n of BD, connect c1n, Mn, C1M. Obviously, BC1 = DC1, BM = DM. So c1n ⊥ BD, Mn ⊥ BD. so ∠ c1nm is the plane angle of dihedral angle m-bd-c1. If the edge length of cube is 2a, it is easy to calculate, C1M = 3A, C1b = √ 6a, MB = √ 3a
RELATED INFORMATIONS
- 1. As shown in the figure, in the cube ABCD – a1b1c1d1, verify that plane aca1c1 is perpendicular to plane a1bd
- 2. Make a plane intersection aa1d1d through the edge BB1 of square abcd-a1b1c1d1, and verify: EF / / BB1
- 3. In cube ABCD_ In a1b1c1d1, if the edge length is a, P is the midpoint of edge Aa1, and Q is any point on edge BB1, then the minimum value of PQ + QC is?
- 4. In the cube abcd-a1b1c1d1, e is the midpoint of d1d, f is the midpoint of AB, and EC is at an angle with FB1
- 5. As shown in the figure, the square prism abcd-a1b1c1d1 is known, the point E is the midpoint of edge d1d, A1A = radical 2a, ab = A. (1) verification: D1
- 6. As shown in the figure, in the four prism abcd-a1b1c1d1, d1d ⊥ bottom surface ABCD, bottom surface ABCD is square, and ab = 1, d1d = 2. (1) find the angle between the line D1b and the plane ABCD; (2) prove: AC ⊥ plane bb1d
- 7. In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, then In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, the area of quadrilateral a1b1c1d1 is ()
- 8. In the cube abcd-a1b1c1d1, e and F are the midpoint of edge BC and c1d1 respectively （2）AC⊥EF (3) Plane aa1c1c ⊥ plane ab1d1
- 9. In a right triangle, the ratio of an acute angle to a right angle is 2:5. What is the degree ratio of this acute angle to another acute angle?
- 10. How many days does it take to reach 5500km from Mohe in the north to Zengmu in the south? In the clouds of the White Emperor, the river mausoleum is still thousands of miles away. The ape on both sides of the river can't stop singing, and the boat has passed the mountains. Taking the light boat as a reference, the overlapping peaks on both sides are still. If you want to move as fast as the boat described by the poet, how many days will it take for you to start from Mohe in the north of China to reach Zengmu dark sand in the south, with a total length of 5500km?
- 11. In the cube abcd-a1b1c1d1, M is the midpoint of Aa1
- 12. In the cube abcd-a1b1cid1, M is the midpoint of CC1, AC intersects BD at O, and it is proved that a1o is perpendicular to the plane MBD How to prove that a1o is perpendicular to BD, BM
- 13. The edge length of cube abcd-a1b1c1d1 is a, and the area of triangle ab1d1 is calculated The edge length of cube abcd-a1b1c1d1 is a, (1) the area of triangle ab1d1, (2) the area of triangular pyramid a1-abd, (3) the sine value of the angle between straight line AC1 and plane ABCD
- 14. It is known that in the cube abcd-a1b1c1d1, the edge length is 1 and the area of triangle a1bc is calculated
- 15. For a cube with shuttle length of 2, in ABCD A1 B1 C1 D1, M is the middle point of edge Aa1, and the area of the cross section is 0 The answer is 9 / 2 I don't know. The answer in the book is 9 / 2
- 16. (1) In the cube abcd-a1b1c1d1, e and F are the moving points on edges BB1 and CC1 respectively, ab = 1. The volume of the tetrahedron with vertices a, C, B1 and D1 is calculated RT
- 17. In the cube abcd-a1b1c1d1, e and F are the midpoint of dd1 and DB, respectively
- 18. In the cube abcd-a1b1c1d1, e is the midpoint of CC1, AC ∩ BD = 0
- 19. In the cube abcd-a.b.c.d., e is the midpoint of AA. Proof: A.C flat plane BDE
- 20. It is known that in the cube abcd-a1b1c1d1, e and F are the midpoint of CC1 and Aa1 respectively