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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

  • VECTORS: Question 3 Go to full solutionGo to Markers CommentsGo to Vectors MenuReveal answer onlyEXIT

  • VECTORS: Question 3 Go to full solutionGo to Markers CommentsGo to Vectors MenuReveal answer onlyEXIT|PA| = 29|PB| = 106APB

  • Markers CommentsBegin SolutionContinue SolutionQuestion 3 Vectors MenuBack to Home====Find the components of PA & PB and hence the size of angle APB.

  • Markers CommentsBegin SolutionContinue SolutionQuestion 3 Vectors MenuBack to HomeFind the components of PA & PB and hence the size of angle APB. (b) Let angle APB = = (-2 X 3) + (4 X 4) + (3 X 9)= -6 + 16 + 27= 37

  • Markers CommentsBegin SolutionContinue SolutionQuestion 3 Vectors MenuBack to HomeFind the components of PA & PB and hence the size of angle APB. 37= 29= 106so = cos-1(37 29 106) = 48.1

  • ExSuppose that AB = ( ) 3-1and BC = ( ) .58Find the components of AC .AC = AB + BC =********( ) + ( ) 3-158= ( ) .87ExSimplifyPQ - RQ********PQ - RQ= PQ + QR= PR