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Math Help - Vector

  1. #1
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    Vector

    The point A and B have coordinates (2,3,-1) and (5,-2,2) respectively. Calculate the acute angle between AB and the line with equation
    r=(2,3,-1)+t(1,-2,2), giving your answer correct to the nearest degree.


    All i need to know is which two to multiply
    e.g: (x,y,z) x (x1,y1,z1)
    (MY PROBLEM IS HOW TO FIND OR WHICH TWO POINTS TO MULTIPLY)

    the i know how to continue
    Thanks in advance.
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  2. #2
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    Quote Originally Posted by manutd4life View Post
    The point A and B have coordinates (2,3,-1) and (5,-2,2) respectively. Calculate the acute angle between AB and the line with equation r=(2,3,-1)+t(1,-2,2), giving your answer correct to the nearest degree.
    The angle is \arccos \left( {\frac{{\left| {\overrightarrow {AB}  \cdot D} \right|}}{{\left\| {\overrightarrow {AB} } \right\|\left\| D \right\|}}} \right) where D is the direction vector of the line.
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  3. #3
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    is AB=AO+OB
    =(-2,-3,1)+(5,-2,2)
    =(3,-5,3)

    let x=(3,-5,3) and y=(1,-2,2)

    (3,-5,3).(1,-2,2)
    =3+10+6
    =19

    so i use |x|.|y|.cos o=19

    Is this good plz help
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  4. #4
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    Quote Originally Posted by manutd4life View Post
    is AB=AO+OB
    =(-2,-3,1)+(5,-2,2)
    =(3,-5,3)
    NO! \overrightarrow {AB}  = \left\langle {5, - 5,3} \right\rangle

    Surely you know how to find the vector determined by two points?
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  5. #5
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    can u explain how u got this plz, cause i forgot a bit
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  6. #6
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    Quote Originally Posted by manutd4life View Post
    can u explain how u got this plz, cause i forgot a bit
    P:\left( {p_1 ,p_2 ,p_3 } \right)\;\& \,Q:\left( {q_1 ,q_2 ,q_3 } \right)\, \Rightarrow \,\overrightarrow {PQ}  = \left\langle {q_1  - p_1 ,q_2  - p_2 ,q_3  - p_3 } \right\rangle
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  7. #7
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    can u tell me what the answer??
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  8. #8
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    Quote Originally Posted by manutd4life View Post
    can u tell me what the answer??
    Sorry, but no I cannot. I am not willing to do the tedious work it takes.
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