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    Just spent hours trying to sove this one, can anybody assist please?
    The points A and B have position vectors i + 2j + 2K and 4i + 3j respectively.

    A point C divides AB in the ratio λ : 1-λ
    Find an expression for OC.

    Book answer is: {1+3λ}i + {2 + λ}j + 2{1-λ}k
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    Just spent hours trying to sove this one, can anybody assist please?
    The points A and B have position vectors i + 2j + 2K and 4i + 3j respectively.

    A point C divides AB in the ratio λ : 1-λ
    Find an expression for OC.
    OA = i + 2j + 2k

    OB = 4i + 3j

    AB = AO + OB = -i -2j -2k +4i +3j = 3i + j - 2k

    AC = λ(3i + j -2k) = 3λi +λj -2λk

    OA + AC = OC = {3λ + 1}i + {λ + 2}j + {2 - 2λ}k
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    (Original post by xlaser31)
    Just spent hours trying to sove this one, can anybody assist please?
    The points A and B have position vectors i + 2j + 2K and 4i + 3j respectively.

    A point C divides AB in the ratio λ : 1-λ
    Find an expression for OC.

    Book answer is: {1+3λ}i + {2 + λ}j + 2{1-λ}k

    C is clearly between AB
    The question is telling us that AC: CB are in the ratio λ:1-λ
    That is, AC(1-λ)=CB(λ)
    (1-λ)[OC-OA]=λ(OB-OC)
    (1-λ)(OC)-(1-λ)(OA)=λ(OB)-λ(OC)
    OC(1-λ+λ)=λ(OB)+(1-λ)(OA)
    OC=λ(4i+3j+0k)+(1-λ)(i+2j+2k)
    OC=i(4λ+1-λ)+j(3λ+2-2λ)+k(2-2λ)
    OC=i(1+3λ)+j(2+λ)+k[2(1-λ)]

    If you click 'reply', as if you were to quote me, then the above is readable.
 
 
 
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