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    can anyone give me a hard vector question?
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    (Original post by berivan123)
    can anyone give me a hard vector question?
    It wouldn't be on a GCSE paper but something like this can be challenging for most GCSE students:

    Use vectors to prove that joining the midpoints of the sides of any quadrilateral will form a parallelogram.
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    a)
    The lines  l_1 and  l_2 have vector equations

     \displaystyle r=\begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix} + \lambda \begin{bmatrix} 1 \\ 1 \\4 \end{bmatrix}
    and
     \displaystyle r= \begin{bmatrix} 2 \\ -1 \\ 0 \end{bmatrix} + \mu \begin{bmatrix} 1 \\ -2 \\ 0 \end{bmatrix}
    respectively.

    Show that the line  l_1 and  l_2 do not intersect.

    b)

    Find the shortest distance between the lines  l_1 and  l_2 .

    (You may not use the vector product or any standard formula that calculates the distance between lines in this question).
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    (Original post by B_9710)
    ...
    Could be a bit too advanced for GCSE level
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    1. Show that the angle between any two faces of a regular octahedron is \arccos \left(-\frac{1}{3}\right).

    2. Find the ratio of the volume of a rectangular octahedron to the volume of the cube whose vertices are the centres of the faces of the octahedron.
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    (Original post by notnek)
    Could be a bit too advanced for GCSE level
    I know, I didn't realise it was a GCSE thread until after I'd posted.
 
 
 
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