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    OK basically i don't get this whole scalar product deal, so can someone explain 2 me how 2 approach these sorts of problems:

    Use a vector method 2 prove that the diagonals of the square OABC cross at right angles.

    So i know i have 2 show that the scalar product of the diagonals = 0 (right?) but how do i do that?

    Any help much appreciated
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    OA=[a,0]
    OB=[0,a]
    OC=[a,a]

    Diagonals are the lines OC and AB

    AB=[0,a]-[a,0]=[-a,a]

    AB.OC=(a*-a)+(a*a)=a2-a2=0 therefore they're perpendicular.
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    Draw a square, say length r. label each corner ABCD.

    If i label it that way clockwise starting from the bottom left, then AC= (r,r) BD= (r,-r).

    AC.BD= r*r - r*r=0 so the diagonals are perpendicular.

    This one is pretty straightforward. There's another one where you have to prove the triangle formed from the diameter of a circle to the circumference, is always a right-angle.

    Use a similar method but call the centre (0,0), see how you get on. A few pointers: call the point from the ends of the diameter to the circumference, point X. Then write the cordinates of X in general terms using r (the radius) and may be x and y which could be your horizontal and vertical distances from O.
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    Is this Edexcel C4? I don't remember having to do either of these proofs.
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    (Original post by Kernel)
    Is this Edexcel C4? I don't remember having to do either of these proofs.
    Yes, its in the excercise. They're not difficult its just that we are not accustomed to these type of questions.
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    Im stuck on a, i *think*, similar sort of problem.

    L : (2i-3j+3k)
    M : (5i+j+ck) , where c is a constant

    The point N is such that OLMN is a rectangle.

    a) find the value of c
    b) Write down the postion vector N
    c) find an equation for line MN

    Im stuck on the first part
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    L and M meet at the corner of the rectangle, so they're perpendicular.
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    Again picture or draw a rectangle. You can see that LM=ON or LO=MN.

    If you use the first, find LM then add O (which is just (0,0,0)).
    Or the second, find LO (which is just multiplying it through by -1) then add M.
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    (Original post by Kernel)
    L and M meet at the corner of the rectangle, so they're perpendicular.

    LM do not meet at a corner.

    If you use the first, find LM then add O (which is just (0,0,0)).
    Or the second, find LO (which is just multiplying it through by -1) then add M.
    I found LM , i dont understand how adding O to this would give me c ?
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    LO and LM are perpedicular. dot product to find c as LO.LM=0

    the bit above is for the second part.
 
 
 
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