Please give detail as much as possible. 1. The unit cube \( \mathbb{Q} \) in the first octant has vertices at \( (1, 0, 0), (0, 0, 0), (0, 1, 0), (1, 1, 0), (1, 0, 1), (0, 0, 1), (0, 1, 1), \) and \( (1, 1, 1) \). The main diagonal of this cube is the line segment connecting the origin with the vertex \( (1, 1, 1) \).(a) Use vectors to calculate the angle between the main diagonal and the line segment connecting the origin and the point \( (0, 1, 1) \).(b) Find a vector which is orthogonal to both of the vectors you considered in part (a).(c) Consider the parallelepiped \( \mathbb{P} \) determined by the main diagonal of \( \mathbb{Q} \), the edge of \( \mathbb{Q} \) which lies on the \( y \)-axis, and the main diagonal of the bottom face of \( \mathbb{Q} \) in the \( xy \)-plane. Compute the volume of this parallelepiped \( \mathbb{P} \).

Name: Please give detail as much as possible. 1. The unit cube \( \mathbb{Q}
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please give detail as much as possible. 1. The unit cube \( \mathbb{Q} \) in the first octant has vertices at \( (1, 0, 0), (0, 0, 0), (0, 1, 0), (1, 1, 0), (1, 0, 1), (0, 0, 1), (0, 1, 1), \) and \( (1, 1, 1) \). The main diagonal of this cube is th