Question

1) Figure below shows a frame {B} that is rotated relative to frame {A} about Z by 30 degrees. Here, Z is pointing out of the page. Given point P in coordination system B, find its coordinate in system A. a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T 2) Coordinatio system {B} that is rotated relative to coordination {A} about Y by 45 degrees. Given point P in coordination system B, find its coordinate in system A. a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T 3) Figure below shows a frame {B}, which is rotated relative to frame {A} about Z by 30 degrees, translated 10 units in XA, and translated 5 units in YA. Find ponit P in coordination system A, where a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T 4) Consider two rotations, one about Z by 30 degrees and one about X by 30 degrees. Find the H matrices for the following sequences of rotations and determine whether thery equivalent or not. a) Rot(Z, 30°)×Rot(X, 30°) b) Rot(X, 30°)×Rot(Z, 30°) 5) A vector Ap is rotated about ZA by ? = 25 degrees and is subsequently rotated about XA by ? = 50 degrees. Give the rotation matrix that accomplishes these rotations in the given order. 6) A vector Ap is rotated about YA by 30 degrees and is subsequently rotated about XA by 45 degrees. Give the rotation matrix that accomplishes these rotations in the given order. 7) A frame {B} is located initially coincident with a frame {A}. We rotate {B} about ZB by ? = 35 degrees, and then we rotate the resulting frame about XB by ? = 70 degrees. Give the rotation matrix that will change the descriptions of vectors from Bp to Ap 8) A frame {B} is located initially coincident with a frame {A}. We rotate {B} about ZB by 30 degrees, and then we rotate the resulting frame about XB by 45 degrees. Give the rotation matrix that will change the description of vectors from Bp to Ap.

          1) Figure below shows a frame {B} that is rotated relative to frame {A} about Z by 30 degrees. Here, Z is pointing out of the page.

Given point P in coordination system B, find its coordinate in system A.
a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T

2) Coordinatio system {B} that is rotated relative to coordination {A} about Y by 45 degrees. Given point P in coordination system B, find its coordinate in system A.
a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T

3) Figure below shows a frame {B}, which is rotated relative to frame {A} about Z by 30 degrees, translated 10 units in XA, and translated 5 units in YA. Find ponit P in coordination system A, where
a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T

4) Consider two rotations, one about Z by 30 degrees and one about X by 30 degrees. Find the H matrices for the following sequences of rotations and determine whether thery equivalent or not.
a) Rot(Z, 30°)&#215;Rot(X, 30°) b) Rot(X, 30°)&#215;Rot(Z, 30°)

5) A vector Ap is rotated about ZA by ? = 25 degrees and is subsequently rotated about XA by ? = 50 degrees. Give the rotation matrix that accomplishes these rotations in the given order.

6) A vector Ap is rotated about YA by 30 degrees and is subsequently rotated about XA by 45 degrees. Give the rotation matrix that accomplishes these rotations in the given order.

7) A frame {B} is located initially coincident with a frame {A}. We rotate {B} about ZB by ? = 35 degrees, and then we rotate the resulting frame about XB by ? = 70 degrees. Give the rotation matrix that will change the descriptions of vectors from Bp to Ap

8) A frame {B} is located initially coincident with a frame {A}. We rotate {B} about ZB by 30 degrees, and then we rotate the resulting frame about XB by 45 degrees. Give the rotation matrix that will change the description of vectors from Bp to Ap.

1) Figure below shows a frame B that is rotated relative to frame A about Z by 30 degrees. Here, Z is pointing out of the page.

Given point P in coordination system B, find its coordinate in system A.
a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T

2) Coordinatio system B that is rotated relative to coordination A about Y by 45 degrees. Given point P in coordination system B, find its coordinate in system A.
a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T

3) Figure below shows a frame B, which is rotated relative to frame A about Z by 30 degrees, translated 10 units in XA, and translated 5 units in YA. Find ponit P in coordination system A, where
a) PB=[0, 2, 0]T b) PB=[2, 1, 0]T c) PB=[0, 2, -1]T d) PB=[1, -2, 3]T

4) Consider two rotations, one about Z by 30 degrees and one about X by 30 degrees. Find the H matrices for the following sequences of rotations and determine whether thery equivalent or not.
a) Rot(Z, 30°) #215;Rot(X, 30°) b) Rot(X, 30°) #215;Rot(Z, 30°)

5) A vector Ap is rotated about ZA by ? = 25 degrees and is subsequently rotated about XA by ? = 50 degrees. Give the rotation matrix that accomplishes these rotations in the given order.

6) A vector Ap is rotated about YA by 30 degrees and is subsequently rotated about XA by 45 degrees. Give the rotation matrix that accomplishes these rotations in the given order.

7) A frame B is located initially coincident with a frame A. We rotate B about ZB by ? = 35 degrees, and then we rotate the resulting frame about XB by ? = 70 degrees. Give the rotation matrix that will change the descriptions of vectors from Bp to Ap

8) A frame B is located initially coincident with a frame A. We rotate B about ZB by 30 degrees, and then we rotate the resulting frame about XB by 45 degrees. Give the rotation matrix that will change the description of vectors from Bp to Ap.

Added by Jose Luis S.

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