Question 2 (12 marks)

(a)

By using dot product of two vectors, each component of AR can be written as the dot

product of a pair of unit vectors:

[&B &₁ PB &₁ 28 &₁]

AR=&B - P₁ PB-PA 28 P₁

XB-2₁ 8/B 2A 2B-2₁

Appraise the geometrical interpretation of the first row:

[&B &₁ PB ₁ 28.₁1

(Ⓒ)

[B]

2₂

2₁

AT =

[4]

Figure 02(a)

(b)

In a coordinate transformation, Frame {A} is transformed to Frame {B}. The resulting

transformation matrix T is given in the following matrix form with numerical values.

P₂

[1 0

0 0.866

0 0.500

Lo 0

P₁

0 51

-0.500 1

0.866 0

0

If the position of point P in Frame {B} is expressed as P = [111]", calculate

the coordinates of point P in Frame {A}.

Appraise by providing your description to show how the Frame {A} can be

transformed to obtain Frame {B} according to the numerical values given in the

AT.

What does the symbol R denote? Analyse the numerical result for R based

on the given condition in T.