91Ó°ÊÓ

The vertices of the tetrahedron correspond to alternating corners of a cube with coordinates (0,0,0), (1,1,0), (1,0,1), and (0,1,1). The center of the cube has coordinates (0.5, 0.5, 0.5). We can find vectors A and B connecting vertices to the center, which are (0.5, 0.5, -0.5) and (0.5, -0.5, 0.5). The dot product of these vectors is -0.25, and their magnitudes are both \(\frac{\sqrt{3}}{2}\). Using the dot product and magnitudes, we find the cosine of the angle between the vectors to be -\(\frac{1}{3}\), and taking the arccosine of this value gives us the angle of approximately \(109.5^{\circ}\). This result confirms that the angle formed by connecting two vertices of the tetrahedron to the center of the cube is consistent with the characteristic angle for tetrahedral molecules.