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

Transcribed Image Text:

By using dot product of two vectors, each component of ABR can be written as the dot product of a pair of unit vectors: AR = [B A B A 8B YA B A 2B A] 2B YA B ZA B ZA ZB ZA . Appraise the geometrical interpretation of the first row: [B A B A B A ] [B] [A] ZB ZA A XB Figure Q2(a) In a coordinate transformation, Frame {A} is transformed to Frame {B}. The resulting transformation matrix BT is given in the following matrix form with numerical values. 1 0 0 0.866 0 5 -0.500 1 BT = 0 0.500 0.866 LO 0 0 1 (i) (ii) (iii) If the position of point P in Frame {B} is expressed as BP = [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 T. What does the symbol AR denote? Analyse the numerical result for BR based on the given condition in BT. By using dot product of two vectors, each component of ABR can be written as the dot product of a pair of unit vectors: AR = [B A B A 8B YA B A 2B A] 2B YA B ZA B ZA ZB ZA . Appraise the geometrical interpretation of the first row: [B A B A B A ] [B] [A] ZB ZA A XB Figure Q2(a) In a coordinate transformation, Frame {A} is transformed to Frame {B}. The resulting transformation matrix BT is given in the following matrix form with numerical values. 1 0 0 0.866 0 5 -0.500 1 BT = 0 0.500 0.866 LO 0 0 1 (i) (ii) (iii) If the position of point P in Frame {B} is expressed as BP = [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 T. What does the symbol AR denote? Analyse the numerical result for BR based on the given condition in BT.