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In the triangle below OA =a and OB=b. M is mid-point of Ab and N is a point on Ob such that ON=1/3OB. AN and OM intersect at P
        

  1. Express the following vectors in terms of a and b
    1. AB 
    2. OM   
    3. AN  
  2. If OP=tOM and AP=sAN, express OP in two different ways hence find the values of t and s. 
  3. State the ratio AN:NP

1 Answer

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  1.  
    1. AB b − a
    2. OM ½a + ½b
    3. AN 1/3b − a
  2.  →
    OP =t(½a + ½b)

    OP = + s(1/3b − a)
    ½t = 1 − s ....(i)
    ½t = 1/3s ....(ii)
    ½t = 1 − 3/2t
    4/2t = 1
     t ½=
      ¼ = 1/3s
        s=¾
  3. AN:NP
       4:−1
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