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As shown in the figure, in the cube abcd-a1b1c1d1, if e and F are the midpoint of A1B1 and b1c1 respectively, then the angle between AD1 and EF is______ ．
As shown in the figure, if a1c1 and AC are connected, then ∵ E and F are the midpoint of A1B1 and b1c1 respectively, ∵ EF ∥ a1c1, ∵ AC ∥ a1c1, ∵ EF ∥ AC ∥ d1ac (or its complementary angle) is the angle formed by the out of plane straight line AD1 and ef. In △ d1ac, D1A = d1c = AC, ∵ d1ac = 60 °, so the answer is: 60 °
As shown in the figure, in the cube abcd-a1b1c1d1, if e and F are the midpoint of A1B1 and b1c1 respectively, then the angle between AD1 and EF is______ ．
As shown in the figure, if a1c1 and AC are connected, then ∵ E and F are the midpoint of A1B1 and b1c1 respectively, ∵ EF ∥ a1c1, ∵ AC ∥ a1c1, ∵ EF ∥ AC ∥ d1ac (or its complementary angle) is the angle formed by the out of plane straight line AD1 and ef. In △ d1ac, D1A = d1c = AC, ∵ d1ac = 60 °, so the answer is: 60 °
RELATED INFORMATIONS
- 1. In the cube abcd-a1b1c1d1, the cosine of the dihedral angle formed by plane a1bd and plane c1bd is () A. 12B. 13C. 32D. 33
- 2. In the cuboid abcd-a'b'c'd ', P and R are the moving points on BB' and CC ', respectively. When P and R satisfy what conditions, PR is parallel to the plane ab'd
- 3. As shown in the figure, in the cube abcd-a1b1c1d1, the tangent of the dihedral angle b-a1c1-b1 is___ ．
- 4. As shown in the figure, in the cuboid abcd-a1b1c1d1, ab = ad = 1, Aa1 = 2, and point P is the midpoint of dd1. Prove: (1) straight line BD1 ‖ plane PAC; (2) plane bdd1 ⊥ plane PAC; (3) straight line PB1 ⊥ plane PAC
- 5. As shown in the figure, the area of square ABCD is 16, △ Abe is an equilateral triangle, point E is in square ABCD, and there is a point P on diagonal BD, so that the sum of PC + PE is minimum, then the minimum value is () A. 4B. 23C. 26D. 2
- 6. In the cube ABCD -- a'b'c'd ', O is the center of the square ABCD on the bottom, and M is the midpoint of the line a'b Verification: plane a'bd ⊥ plane a'acc ' emergency
- 7. As shown in the figure, in the pyramid p-abcd with rectangular bottom, PA ⊥ plane ABCD, PA = ad, e is the midpoint of PD (1) verification: Pb ∥ plane AEC; (2) verification: plane PDC ⊥ plane AEC
- 8. As shown in the figure, in the square ABCD with side length of 5 + 2, draw a sector with a as the center, draw a circle with o as the center, m, N, K as the tangent points, take the sector as the side of the cone, and take the circle O as the bottom of the cone to form a cone, and calculate the total area and volume of the cone
- 9. In the parallelogram ABCD, a (1,1) AB vector (6,0) m is the midpoint of line AB, and the intersection of line cm and BD is p I know that the trajectory of P is a circle, but I don't know how to prove it
- 10. In the parallelogram ABCD, point m is the midpoint of AB, point n is on BD and BN = 1 / 3bd. It is proved that m, N and C are collinear 0 Use vectors if you can
- 11. It is known that the parallelepiped abcd-a'b'c'd ', e, F, G and H are the midpoint of edges a'd', d'c ', c'c and ab respectively. It is proved that e, F, G, h are coplanar
- 12. In the cube abcd-a1b1c1d1 with edge length of 2, e is the midpoint of edge AB, and point P is in plane a1b1c1d1. If d1p ⊥ plane PCE, try to find the direction of line d1p My answer is 4 root 5 / 5 is correct?
- 13. As shown in the figure, in the quadrilateral ABCD and the quadrilateral a1b1c1d1, if AB = A1B1, BC = b1c1, CD = c1d1, Da = d1a1, are the two quadrilateral congruent 1. XiaoCong's idea: connect diagonal AC and a1c1 respectively. If AC = a1c1, then The two quadrangles are congruent. According to Xiao Cong's idea, write the reasoning process 2. The teacher said that under the condition that the four sides of the quadrilateral are equal, Xiao Cong Add a condition - diagonal AC = a1c1, you can show congruence Please add another condition (except diagonal) to explain the congruence of the two quadrangles and write down your thinking process
- 14. The bottom surface of straight quadrangular prism ABCD --- a1b1c1d1 with height of 1 is a diamond with area of 2 The area sum of BDD 1B1 is 5, and the bottom edge length of the straight quadrangular prism is calculated
- 15. A prism whose side edge is perpendicular to the bottom is called a straight prism. It is known that the bottom is a rhombic straight prism. Its volume diagonals are 9 and 15 respectively, and its height is 5
- 16. A prism whose side edge is perpendicular to the bottom is called a straight prism. It is known that the bottom is a rhombic straight prism. Its volume diagonals are 9 and 15 respectively, and its height is 5
- 17. If the side length of diamond ABCD is 5cm and one diagonal is 6cm, the area of diamond ABCD is 5cm___ cm2．
- 18. In the cube abcd-a1b1c1d1 each vertex and each edge midpoint total 20 points, take any 2 points to form a straight line, take any one of these straight lines, the probability that it is perpendicular to the diagonal BD1 is () A. 21166B. 21190C. 18190D. 27166
- 19. As shown in the figure, the edge length of cube abcd-a1b1c1d1 is 4, M is the midpoint of BD1, n is on a1c1, and | A1N | = 3 | NC1 |, then the length of Mn is___ ．
- 20. The area of square ABCD is 200 square centimeters. Find the area of inscribed circle (π = 3.14)