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# C4 Vectors watch

1. 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
2. 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.
3. 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.
4. Is this Edexcel C4? I don't remember having to do either of these proofs.
5. (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.
6. 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
7. L and M meet at the corner of the rectangle, so they're perpendicular.
8. 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.
9. (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 ?
10. 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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Updated: June 13, 2006
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