How to set up a rectangular coordinate system for a pyramid whose base side length is 5, root 2, and side edge length is 13?
If the bottom is a square, the center is the left inner fixed point, the height is the Z axis, the outer side is the X axis, and the left side is the Y axis
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- 1. It is known that the three sides of △ ABC are a = 2, radical 5, B = radical 13 and C = radical 61. Try to find the area of △ ABC Associative figure
- 2. It is known that △ ABC ∽ def, the lengths of three sides of △ ABC are radical 2, radical 14, 2, and the lengths of two sides of △ def are 1 and radical 7 respectively, so the third side of △ def can be obtained To solve the process
- 3. In tetrahedral PABC, PA, Pb and PC are perpendicular. It is proved that △ ABC is an acute triangle In tetrahedral PABC, PA, Pb and PC are perpendicular. It is proved that ① △ ABC is an acute triangle. ② the square of s △ ABC = the square of s △ PBC + the square of s △ PAB + the square of s △ PCA
- 4. P is a point in the equilateral triangle ABC. If the distance from P to three sides is equal, then PA = Pb = PC Please prove this proposition,
- 5. In the isosceles triangle ABC, ab = AC = 6, P is a point on BC, and PA = 4, then what is the value of Pb × PC?
- 6. If we know three vertices a, B, C of ⊿ ABC and a point P in the plane, satisfying PA + Pb + PC = 0, then point P is () A. Center of gravity
- 7. Given three vertices a, B, C of △ ABC and a point P in the plane, if the vector PA + Pb + PC = AB, then the positional relationship between point P and △ ABC is? The relationship between PA and PC is obtained
- 8. Each vertex of the cuboid abcd-a1b1c1d1 is on the sphere of the sphere o with the volume of 32 / 3 Pai, where Aa1 = 2, then the volume of the pyramid o-abcd is smaller The maximum value is
- 9. If the five vertices of the pyramid p-abcd are on the same sphere, and the bottom surface is a square with side length 4, PA is perpendicular to ABCD, PA = 2, then the surface area of the sphere can be obtained
- 10. What is the volume of a regular triangular pyramid if its four vertices are on a sphere of radius 1, and the three vertices of its bottom are on a big circle of the sphere
- 11. The bottom of the Mitsubishi cone is an equilateral triangle with side length a, and the length of the two sides is (root number 13) a / 2. Try to find the value range of the third side length
- 12. It is known that the base of a triangular pyramid is an equilateral triangle with side length of 1, and the length of the two side edges is 2 / 13, then the length of the third edge is equal
- 13. Let the length of six edges of a tetrahedron be 1,1,1,1, a, √ 2 respectively, and the edges with length a are different from the edges with length √ 2 around
- 14. What is the volume of a regular tetrahedron with a side length of 3 radical 2?
- 15. The surface area of a pyramid with 1 edge length is
- 16. The volume of a regular pyramid is 2 / 3 of the root sign, and the minimum surface area is obtained
- 17. In solid geometry, if the volume of a triangular pyramid with equal edge length is 2 / 3 of its root sign, the surface area of the pyramid is
- 18. Comparison size: - 1.3 and - root 1.7, 8 / 8 root 10-3 and 1 / 8
- 19. The volume ratio of the inscribed sphere to the circumscribed sphere of a cube is______ .
- 20. The volume ratio of the inscribed sphere to the circumscribed sphere of a cube is______ .