In the parallel hexahedron abcd-a1b1c1d1, the In the parallelepiped abcd-a1b1c1d1, the lengths of the three edges with vertex a as the endpoint are all 1, and their included angles are all 60 ° to each other. The distance between the plane ABCD and a1b1c1d1 is calculated

In the parallel hexahedron abcd-a1b1c1d1, the In the parallelepiped abcd-a1b1c1d1, the lengths of the three edges with vertex a as the endpoint are all 1, and their included angles are all 60 ° to each other. The distance between the plane ABCD and a1b1c1d1 is calculated

The distance between the plane ABCD and a1b1c1d! Is half root 3

In the straight parallelepiped AC1, we know AB = 5, ad = 3, Aa1 = 4, angle DAB = 60 °, what is the length of the diagonal AC1
My answer is the root 65,

Yes
First cosine theorem, then Pythagorean theorem

As shown in the figure, in the cube abcd-a1b1c1d1, the tangent of the dihedral angle b-a1c1-b1 is___ ．

Using the vector method, the solution is as follows: take D1 as the origin, d1a1 as the X axis, d1c1 as the Y axis, d1d as the Z axis, establish the d1-xyz space rectangular coordinate system

In cube AC1, what is the tangent of dihedral angle b-a1c1-b1? Thank you

Using the vector method, the solution is as follows: take D1 as the origin, d1a1 as the X axis, d1c1 as the Y axis, d1d as the Z axis, establish the space rectangular coordinate system of d1xyz. Let the side length of the cube be 1, it is easy to know that a normal vector of plane a1c1b1 is (0,0,1), and A1 (1,0,0), B (1,1,1), C1 (0,1,0) then vector A1B (0,1,1), vector C1b (1,0