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    How should part (c) be done? I found the line connecting A and B, and then equated it to P to find lambda at P, but I'm not sure if this is right.

    Appreciate your help, thanks
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    (Original post by ezioaudi77)


    How should part (c) be done? I found the line connecting A and B, and then equated it to P to find lambda at P, but I'm not sure if this is right.

    Appreciate your help, thanks
    The "point P" is actually the equation of a straight line in disguise...

    if you rearrange it, as in the mark scheme, (and let r denote the straight line) it becomes \mathbf{r} = -9\mathbf{k} + \lambda (\mathbf{i} +2\mathbf{j} + 2\mathbf{k})

    so if you try and imagine it, the question is to actually try and show the points A and B lie on the line r (i.e. show that the points A and B the position vector -9k plus some some scale factor of the direction vector of lambda)
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    (Original post by boner in jeans)
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    When I see "point P", I would never think of it as a vector equation of a line. But your explanation makes sense, thanks
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    I have a vector question if anyone can help please,
    The coordinates of points A,B and C are (4,2,-5), (10,2,-7) and (12,5,9)
    a) find a vector equation of the line l1 that passes through A and B
    I did this and got r=4i + 2j - 5k +lambda(6i + 2k) which is correct

    b) Point X is on l1 such that direction vector CX is perpendicular to AB, find the coordinates of X.

    This is what I'm stuck on, help please!!
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    (Original post by JenniS)
    I have a vector question if anyone can help please,
    The coordinates of points A,B and C are (4,2,-5), (10,2,-7) and (12,5,9)
    a) find a vector equation of the line l1 that passes through A and B
    I did this and got r=4i + 2j - 5k +lambda(6i + 2k) which is correct

    b) Point X is on l1 such that direction vector CX is perpendicular to AB, find the coordinates of X.

    This is what I'm stuck on, help please!!
    OX can be written as (4 +6λ)i + (2)j + (-2 -5λ)k.

    CX = OX - OC.

    If you know the dot product rule, you can find λ by CX∙AB=0.

    Substitute the value you found for λ in (4 +6λ)i + (2)j + (-2 -5λ)k, and you can find the coordinates of X
 
 
 
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