Consider the figure shown in 4 with three frames shown. The figure is a regular tetrahedron with side lengths equal 1 = 1m. The base frame is centrally located under the top vertex with the Ae perpendicular to the edge it is directed towards. The corner frame {B} is located at the vertex with the ge directed along the edge (and colinear with e and B perpendicular to the planar face as shown at the rear of the tetrahedron, as shown in Figure 4. Frame (C) is located at the top vertex oriented symmetrically around the edges. That is the direction 1 - ()- 3 Bel Be {B} Cv= and Eu points directly at frame {A}. The axes ce, ce, and ce, lie as close to the edges as shown as they can. {C} = - G3 ce3 ce {A} Figure 4: A tetrahedron 1 = 1m PA 5. (1 mark) Compute e,: The coordinates of the third axis of {B} expressed in {A}. 6. (1 mark) Compute RB: The orientation of {B} expressed in {A}. 7. (1 mark) Compute BRA: The orientation of {A} expressed in {B}. 8. (1 mark) Compute the pose APB: The pose of {B} with respect to {A} expressed in {A}. Write this as a homogeneous matrix. 9. (1 mark) Compute the pose BPA: The pose of {A} with respect to {B} expressed in {B}. Write this as a homogeneous matrix. 10. (1 mark) Compute BP: the coordinates of p measured with respect to {B} and expressed in {B}. Now consider frame {C} 1. (1 mark) Computero: The coordinates of the origin of {C} with respect to {A} expressed in {A}. 2. (1 mark) Compute e,: The coordinates of the first axis of {C} expressed in {A}. 3. (1 mark) Compute e: The coordinates of the second axis of {C} ex- pressed in {A}. 4. (1 mark) Computee: The coordinates of the third axis of {C} expressed in {A}. 5. (1 mark) Compute Re: The orientation of {C} expressed in {A}. 6. (1 mark) Compute the pose Pc: The pose of {C} with respect to {A} expressed in {A}. Write this as a homogeneous matrix. 7. (1 mark) Compute CP: the coordinates of p measured with respect to {C} and expressed in {C}.