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From a point m on the sphere with radius r, three pairs of perpendicular strings Ma, MB and MC of the leading sphere, then ma2 + MB2 + MC2 equals () A. R2B. 2R2C. 4R2D. 8R2
Ma, MB and MC are perpendicular to each other, so the three line segments are three edges of a cuboid with the same vertex. The diagonal of the cuboid is just the diameter of the circumscribed sphere, ∵ a, B, C and m are the four points on the sphere with radius r, ∵ the diameter of the sphere is 2R, ∵ AB2 + ac2 + ad2 = 4r2
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- 1. What is QC, QA, QE, and what is QB?
- 2. What do QC, QA, QE and QD mean in quality inspection?
- 3. Two charges a and B are placed on the smooth insulating plane in vacuum, with the distance r between them. The charges are QA = + 9q, QB = + Q respectively, and another point charge QC is placed Just so that the three spheres are in equilibrium only under the action of their mutual electrostatic force, what kind of charge should QC carry, where should it be placed, and what is the amount of charge
- 4. The difference between QA and QC
- 5. As shown in the figure, in the pyramid p-abcd, the bottom surface ABCD is a square, the PD ⊥ plane ABCD, and PD = AB = 2, e is the midpoint of Pb 1. Calculate the tangent of the angle between the paint line PD and AE 2. Verification: EF vertical plane PBC 3. Find the cosine value of dihedral angle f-pc-b
- 6. In a square pyramid p-abcd, the plane PCD is perpendicular to the plane ABCD, PC = PD = CD = 2, and the dihedral angle b-pd-c is calculated Urgent! It's a process
- 7. As shown in the figure, in the pyramid p-abcd, the quadrilateral ABCD is a rectangle, the plane PCD ⊥ the plane ABCD, and M is the midpoint of PC
- 8. The perimeter of parallelogram ABCD is 70, the distances AE and AF from vertex a to BC and CD are 10 and 15, respectively
- 9. As shown in the figure, in the cube abcd-a1b1c1d1, P is a moving point in the side bb1c1c. If the distance from P to the straight line BC and the straight line c1d1 is equal, the curve of the trajectory of the moving point P is () A. Straight line B. circle C. hyperbola D. parabola
- 10. In the square abcd-a1b1c1d1, P is a moving point in the side b1b1cc. If the distance from P to the straight line BC and c1d1 is equal, then the trajectory of the moving point P is? Why a parabola?
- 11. The square ABCD is inscribed on the circle O, P is on the inferior arc AB, connecting PD and AC to Q, and PQ = OQ Sorry, I can't draw a picture
- 12. Square ABCD is inscribed in circle O, P is a point on inferior arc BC, AP intersects BD with Q, QP = Qo, and QD / Qo is obtained= We haven't learned similarity and trigonometric functions yet
- 13. As shown in the figure, square ABCD is inscribed in ⊙ o, q is a moving point on diameter AC, connecting DQ and extending intersection ⊙ o to P. if QP = Qo, then the value of QAQC is______ ．
- 14. As shown in the figure, in the parallelogram ABCD, e and F are on AB and ad respectively, and EF intersects AC at point g. if AE: EB = 2:3, AF: ad = 1:2, calculate the value of Ag: AC
- 15. As shown in the figure, in the parallelogram ABCD, e and F are on AB and ad respectively, and EF intersects AC at point g. if AE: EB = 2:3, AF: ad = 1:2, what is the value of Ag: AC
- 16. In the parallelogram ABCD, e is the midpoint of CD, connect be and extend it, intersect the extension line of ad with point F, and prove that e is the midpoint of BF and D is the midpoint of AF
- 17. Let e be the midpoint of AD, a right: b right = 2:3, and find the value of Ag: GC
- 18. Let e be the midpoint of AD, a right: b right = 2:3, and find the value of Ag: GC
- 19. ABCD is a square with side length of 4, e and F are the midpoint of AB and ad, GC is vertical to plane ABCD, GC is equal to 2, find the distance from B to plane EFG?
- 20. There are seven planes with the same distance from the four vertices of the space quadrilateral ABCD