CHAPTER 3 DIFFERENTIATION VECTORS OF The following formulae are useful for the differentiation of sums and products of vectors:  , If and then A  At B  Bt d c dt a) A d A dt c dt dt dt   b) d  B d d A dt   d d A c) A  d B dt dt dt   d  A d) B A    d d B  B dt Example 3.4 2t 2t If 1kˆ 3iˆ , find A  t tˆj   and B   tkˆ ˆj 2iˆ d dt dt b) c) at t=1     A  a) dt dt d d d B 2t a) 3 A B  t t t2t   2 2t 5t  3 2   t1 d d dt dt 6t 10t 2   2 t1 dt dt   d or apply A  A  B  d t d B
CHAPTER 3 DIFFERENTIATION OF VECTORS The following formulae are useful for the differentiation of sums and products of vectors: If A  At  and B  Bt , then a) d dt c A c d A dt b) d dt   d A dt  d B dt c) d) d dt d dt   A    A  d B dt d B dt   d A d A dt  B  B Example 3.4 If A  t 2iˆ tˆj  2t  1kˆ and B  2t 3iˆ  ˆj tkˆ , find a) d dt   b) d dt   c) d dt A  d B dt at t=1 a) A  B  t 2 2t 3 t t2t   2t 3 5t 2 d dt d dt   t1  6t 2 10t 2 t1  or apply d dt   A  d B dt  d A  B t