Question 1 (10 marks)

Figure Q1 shows a coordinate frame {A}. Here X is pointing out of page according to the right-

hand rule. The frame {A} is rotated by 0 = -30° about into a new coordinate frame {B}.

ŽA

{A}

Figure 01

(a) Plot a figure to schematically illustrate the coordinate frame {B} based on the illustration

given in Figure Q1.

(b) List formula to calculate the rotation matrix R and present the numerical result.

(c) Demonstrate that the R matrix is orthonormal by calculation.

(d) A position vector is expressed in {A} as ^P = [012]. Calculate its position in {B}, i.e.,

BP.

(e) A position vector is expressed in {B} as BP = [012]. Calculate its position in {A}, i.e.,

AP.

(f) Calculate determinant of R, i.e., R.