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Math Help - Please help me to solve this vector question.....

  1. #1
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    Please help me to solve this vector question.....

    The position vectors of point A,B and C are 9i-10j , 4i+2j and Ki-2j respectively.Find the value of k if the point A,B and c are collinear. Help me solve this.thank u
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  2. #2
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    Re: Please help me to solve this vector question.....

    What is the vector from A to B? What is the vector from A to C? Do you know what "colinear" means?
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  3. #3
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    Re: Please help me to solve this vector question.....

    Do you know what collinear means?
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  4. #4
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    Re: Please help me to solve this vector question.....

    Hello, sharmala1

    The position vectors of points A, B and C are 9i-10j , 4i+2j and Ki-2j respectively.
    Find the value of k if the points A,B and c are collinear.

    \overrightarrow{BA} \:=\:\langle 5,\,\text{-}12\rangle

    \overrightarrow{BC} \:=\:\langle (K\!-\!4),\,\text{-}4\rangle

    If A,B,C are collinear, then: . \overrightarrow{BA} \parallel \overrightarrow{BC}

    \text{That is: }\:a\cdot\overrightarrow{BC} \:=\:\overrightarrow{BA}\,\text{ for some real number }a \ne0.

    We have: . a\cdot\langle(K\!-\!4),\,\text{-}4\rangle \;=\;\langle5,\,\text{-}12\rangle

    . . . . . . . . . \langle a(K\!-\!4),\,\text{-}4a\rangle \;=\;\langle 5,\,\text{-}12\rangle


    Hence: . \begin{Bmatrix}a(K\!-\!4) &=& 5 & [1] \\ \text{-}4a &=& \text{-}12 & [2] \end{Bmatrix}

    From [2]: . a\,=\,3

    Subtitute into [1]: . 3(K-4) \:=\:5 \quad\Rightarrow\quad K-4\:=\:\tfrac{5}{3}

    Therefore: . K \:=\:\frac{17}{3}

    Thanks from sharmala
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  5. #5
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    Re: Please help me to solve this vector question.....

    Equating the gradients can also be done.
    (9,-10),(4,2),(k,-2)

    m=\frac{2-(-10)}{4-9}=\frac{-2-2}{k-4}

    and solve for k to get what Soroban got.
    Thanks from sharmala
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