(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.
Fig: 1