# vector journeys!

Post on 14-Jan-2017

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• Block 3

Vector Journeys

• What is to be learned?How to get components of a vector using other vectors

• Useful (Indeed Vital!) To KnowParallel vectors with the same magnitude will have the same

If vector AB has components ai + bj + ck, then BA will have components... components-ai bj ck

• DiversionsSometimes needalternative route!ABCDEAE= AB+ BC+ CD+ DE

• DiversionsSometimes needalternative route!ABCDEAE= AB+ BC+ CD+ DE

• DiversionsSometimes needalternative route!ABCDEAE= AB+ BC+ CD+ DE

• DiversionsSometimes needalternative route!ABCDEAE= AB+ BC+ CD+ DE

• Using ComponentsAB = 2i + 4j + 5k and BC = 5i + 8j + 3k

AC = 7i + 12j + 8k

DE = 6i + 5j + k and FE = -3i + 4j + 5k

DF = 9i + j 4k

= AB + BC= DE + EF= 3i 4j 5kEF

• Wee Diagrams and ComponentsABCDABCD is a parallelogramTT is mid point of DCAB = 846( )BC = 351( )ATInfo Given= DC= AD= AD+ DT= AD+ DC351( )423( )+774( )=Find AT

• Wee Diagrams and LettersABCDAB = 4DCuvFind AD in terms of u and v?4u-v-uAD = 4u v u= 3u v

• Vector JourneysFind alternative routes using diversionsWith LettersABCDuvAD = 3BCFind CD in terms of u and vCD= CB+ BA+ AD= -v + u + 3v= 2v + u

• with componentsABCDEEABCD is a rectangular based pyramidTT divides AB in ratio 1:2EC = 2i + 4j + 5kBC = -3i + 2j 3kCD = 3i + 6j + 9kFind ETET= EC+ CB+ BT2/3 of CD12245( )=3 -2 3( )++negative246( )= 7i + 6j + 14k

• Key QuestionABCDABCD is a parallelogramTT is mid point of BCAB = 846( )BC = 462( )DT= DC= DC+ CT= DC+ CB846( )-2 -3 -1 ( )+615( )=Find DT

• QuestionsCunningly Acquired!

• QuitQuitVectors HigherPreviousNextVABCD is a pyramid with rectangular base ABCD.The vectors are given by

Express in component form. Ttriangle rule ACVRe-arrangeTriangle rule ABCalso