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CM_Tutor

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I encourage all MX2 students to have a look at the following thread in the MX1 forum:

https://boredofstudies.org/threads/vector-projections-qs-help-plz-ugrent.394192/

The third question sounds simple but I believe it has been set in error as there is no simple solution. The posts in the thread do explore some aspects of the problem and could be adapted to a problem in proof.

Perhaps as something like:

If is the origin, is a variable point satisfying , and is a triangle of area 10 u2, show that can be located anywhere on the number plane so long as , and find the value of .
 

notme123

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If you have triangle POB:
theta is angle between OB and OP

Since


and since
therfore,

Works as long as B and P aren't collinear i.e.
But since B is variable, for every point P there will be a non-collinear B.
Therefore OP can be anywhere on the number plane as long as
 
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CM_Tutor

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Works as long as B and P are not collinear i.e.
But since B is variable, for every point P there will be a non-collinear B.
B, O, and P can't be collinear and be the vertices of a triangle of non-zero area.

Otherwise, good job! :)
 

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