Need help with understanding the concept to do finish problems some vector algebra, the question are on the picture, if someone could explain step by step or the concepts needed to comprehend this 2 problems, thank you

where H is an angle. 7'. Let 1, 1, it} and h be urtit vectors satisfying 312 _ *1 h] _A [h] i {I} where A costi' sin' _ sin cos ' Assume that the vectors ill and f1 are perpendicular. Draw the 1rectors i2 and f1 dened by {l} and give a geometric representation of the transformation represented by matrix A. 8. 1With the same assumptions as in Prohlerns ti and I consider an arbitrary 1rector V = 3131+E'1?1 (2} = 3232+E'2h: Le, (a. J\") are the components of if when 1.! is expressed in terms of the vectors [11,91], and {chin} are the components of s when 1' is expressed in terms of the 1.rectors [22,53]. Show that [I] and (2) imply that these components satisfy 02 _ costi' sinti' a] _ sin cost! in