How can I answer vector on the triangle












0












$begingroup$


enter image description here




How can I get the vector OP to be this form :




enter image description here




I think that





  • OP = b + t

  • OP = a + s


I do not know how to do this problem, can anyone gives any idea and some steps to solve this ?










share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    enter image description here




    How can I get the vector OP to be this form :




    enter image description here




    I think that





    • OP = b + t

    • OP = a + s


    I do not know how to do this problem, can anyone gives any idea and some steps to solve this ?










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      enter image description here




      How can I get the vector OP to be this form :




      enter image description here




      I think that





      • OP = b + t

      • OP = a + s


      I do not know how to do this problem, can anyone gives any idea and some steps to solve this ?










      share|cite|improve this question









      $endgroup$




      enter image description here




      How can I get the vector OP to be this form :




      enter image description here




      I think that





      • OP = b + t

      • OP = a + s


      I do not know how to do this problem, can anyone gives any idea and some steps to solve this ?







      vector-spaces vectors triangles vector-fields






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Dec 21 '18 at 2:31









      Aster ZenAster Zen

      438




      438






















          1 Answer
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          $begingroup$

          Using your definition of s and t, from triangle OAN we have



          $$vec{OP} = (1 - s)vec{OA} + svec{ON} = (1 - s)vec{a} + frac{1}{3}svec{b}$$



          Hence A = 1, B = 1 and C = 3.



          Also from triangle OBM we have



          $$vec{OP} = tvec{OM} + (1 - t)vec{OB} = frac{3}{4}tvec{a} + (1 - t)vec{b}$$



          Hence D = 3, E = 4 and F = 1.



          By comparing these 2 equations, we have



          $1 - s = frac{3}{4}t$ and $frac{s}{3} = 1 - t$



          The solution is $s = frac{1}{3}$ and $t = frac{8}{9}$



          Therefore $vec{OP} = frac{2}{3}vec{a} + frac{1}{9}vec{b}$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 0:54










          • $begingroup$
            And I wonder how is the PN. OA looks like and how can you get them ?
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 1:36










          • $begingroup$
            Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
            $endgroup$
            – KY Tang
            Dec 23 '18 at 15:22










          • $begingroup$
            Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
            $endgroup$
            – Aster Zen
            Dec 24 '18 at 4:17










          • $begingroup$
            PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
            $endgroup$
            – KY Tang
            Dec 24 '18 at 19:08












          Your Answer





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          1 Answer
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          1 Answer
          1






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          active

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          1












          $begingroup$

          Using your definition of s and t, from triangle OAN we have



          $$vec{OP} = (1 - s)vec{OA} + svec{ON} = (1 - s)vec{a} + frac{1}{3}svec{b}$$



          Hence A = 1, B = 1 and C = 3.



          Also from triangle OBM we have



          $$vec{OP} = tvec{OM} + (1 - t)vec{OB} = frac{3}{4}tvec{a} + (1 - t)vec{b}$$



          Hence D = 3, E = 4 and F = 1.



          By comparing these 2 equations, we have



          $1 - s = frac{3}{4}t$ and $frac{s}{3} = 1 - t$



          The solution is $s = frac{1}{3}$ and $t = frac{8}{9}$



          Therefore $vec{OP} = frac{2}{3}vec{a} + frac{1}{9}vec{b}$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 0:54










          • $begingroup$
            And I wonder how is the PN. OA looks like and how can you get them ?
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 1:36










          • $begingroup$
            Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
            $endgroup$
            – KY Tang
            Dec 23 '18 at 15:22










          • $begingroup$
            Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
            $endgroup$
            – Aster Zen
            Dec 24 '18 at 4:17










          • $begingroup$
            PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
            $endgroup$
            – KY Tang
            Dec 24 '18 at 19:08
















          1












          $begingroup$

          Using your definition of s and t, from triangle OAN we have



          $$vec{OP} = (1 - s)vec{OA} + svec{ON} = (1 - s)vec{a} + frac{1}{3}svec{b}$$



          Hence A = 1, B = 1 and C = 3.



          Also from triangle OBM we have



          $$vec{OP} = tvec{OM} + (1 - t)vec{OB} = frac{3}{4}tvec{a} + (1 - t)vec{b}$$



          Hence D = 3, E = 4 and F = 1.



          By comparing these 2 equations, we have



          $1 - s = frac{3}{4}t$ and $frac{s}{3} = 1 - t$



          The solution is $s = frac{1}{3}$ and $t = frac{8}{9}$



          Therefore $vec{OP} = frac{2}{3}vec{a} + frac{1}{9}vec{b}$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 0:54










          • $begingroup$
            And I wonder how is the PN. OA looks like and how can you get them ?
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 1:36










          • $begingroup$
            Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
            $endgroup$
            – KY Tang
            Dec 23 '18 at 15:22










          • $begingroup$
            Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
            $endgroup$
            – Aster Zen
            Dec 24 '18 at 4:17










          • $begingroup$
            PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
            $endgroup$
            – KY Tang
            Dec 24 '18 at 19:08














          1












          1








          1





          $begingroup$

          Using your definition of s and t, from triangle OAN we have



          $$vec{OP} = (1 - s)vec{OA} + svec{ON} = (1 - s)vec{a} + frac{1}{3}svec{b}$$



          Hence A = 1, B = 1 and C = 3.



          Also from triangle OBM we have



          $$vec{OP} = tvec{OM} + (1 - t)vec{OB} = frac{3}{4}tvec{a} + (1 - t)vec{b}$$



          Hence D = 3, E = 4 and F = 1.



          By comparing these 2 equations, we have



          $1 - s = frac{3}{4}t$ and $frac{s}{3} = 1 - t$



          The solution is $s = frac{1}{3}$ and $t = frac{8}{9}$



          Therefore $vec{OP} = frac{2}{3}vec{a} + frac{1}{9}vec{b}$






          share|cite|improve this answer











          $endgroup$



          Using your definition of s and t, from triangle OAN we have



          $$vec{OP} = (1 - s)vec{OA} + svec{ON} = (1 - s)vec{a} + frac{1}{3}svec{b}$$



          Hence A = 1, B = 1 and C = 3.



          Also from triangle OBM we have



          $$vec{OP} = tvec{OM} + (1 - t)vec{OB} = frac{3}{4}tvec{a} + (1 - t)vec{b}$$



          Hence D = 3, E = 4 and F = 1.



          By comparing these 2 equations, we have



          $1 - s = frac{3}{4}t$ and $frac{s}{3} = 1 - t$



          The solution is $s = frac{1}{3}$ and $t = frac{8}{9}$



          Therefore $vec{OP} = frac{2}{3}vec{a} + frac{1}{9}vec{b}$







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 23 '18 at 15:21

























          answered Dec 21 '18 at 19:33









          KY TangKY Tang

          50436




          50436












          • $begingroup$
            Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 0:54










          • $begingroup$
            And I wonder how is the PN. OA looks like and how can you get them ?
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 1:36










          • $begingroup$
            Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
            $endgroup$
            – KY Tang
            Dec 23 '18 at 15:22










          • $begingroup$
            Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
            $endgroup$
            – Aster Zen
            Dec 24 '18 at 4:17










          • $begingroup$
            PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
            $endgroup$
            – KY Tang
            Dec 24 '18 at 19:08


















          • $begingroup$
            Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 0:54










          • $begingroup$
            And I wonder how is the PN. OA looks like and how can you get them ?
            $endgroup$
            – Aster Zen
            Dec 22 '18 at 1:36










          • $begingroup$
            Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
            $endgroup$
            – KY Tang
            Dec 23 '18 at 15:22










          • $begingroup$
            Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
            $endgroup$
            – Aster Zen
            Dec 24 '18 at 4:17










          • $begingroup$
            PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
            $endgroup$
            – KY Tang
            Dec 24 '18 at 19:08
















          $begingroup$
          Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
          $endgroup$
          – Aster Zen
          Dec 22 '18 at 0:54




          $begingroup$
          Oh I get more insights, thxu, but I am confused bcs the right answer is : s= 1/3 and t = 8/9
          $endgroup$
          – Aster Zen
          Dec 22 '18 at 0:54












          $begingroup$
          And I wonder how is the PN. OA looks like and how can you get them ?
          $endgroup$
          – Aster Zen
          Dec 22 '18 at 1:36




          $begingroup$
          And I wonder how is the PN. OA looks like and how can you get them ?
          $endgroup$
          – Aster Zen
          Dec 22 '18 at 1:36












          $begingroup$
          Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
          $endgroup$
          – KY Tang
          Dec 23 '18 at 15:22




          $begingroup$
          Sorry to have made a mistake by missing an 's' in the first equation. Now is fixed as shown above.
          $endgroup$
          – KY Tang
          Dec 23 '18 at 15:22












          $begingroup$
          Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
          $endgroup$
          – Aster Zen
          Dec 24 '18 at 4:17




          $begingroup$
          Oh alright thanks, but can you give more explanation about what PN x OA looks like ?
          $endgroup$
          – Aster Zen
          Dec 24 '18 at 4:17












          $begingroup$
          PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
          $endgroup$
          – KY Tang
          Dec 24 '18 at 19:08




          $begingroup$
          PN = (1-s)AN =(1-s)(AO+ON) = (1-s)(-a+b/3)=-2a/3+2b/9 Also OA=a
          $endgroup$
          – KY Tang
          Dec 24 '18 at 19:08


















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