ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: suskieanna on March 04, 2019, 08:33:52 pm
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Hello I am struggling with this question. Can anyone help me with this question? I will really appreciate it if you do :)
3. Points A and B are defined by the position vectors a = 2i - 2j - k and b = 3i + 4k.
b) Find the unit vector which bisects angle AOB.
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Hello I am struggling with this question. Can anyone help me with this question? I will really appreciate it if you do :)
3. Points A and B are defined by the position vectors a = 2i - 2j - k and b = 3i + 4k.
b) Find the unit vector which bisects angle AOB.
Use the fact that diagonals of a parallelogram bisect the interior angles.
Can you use the position vectors a and b to find a point C such that OACB is a parallelogram? From there the problem is straightforward.
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Use the fact that diagonals of a parallelogram bisect the interior angles.
Can you use the position vectors a and b to find a point C such that OACB is a parallelogram? From there the problem is straightforward.
The question first asked to find the unit vector of a and the unit vector of b.
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The question first asked to find the unit vector of a and the unit vector of b.
I don't think that's obviously helpful, because the sum of two unit vectors is, in general, not a unit vector.
The most straightforward way to do this problem is to just use a and b to find a vector that gives the diagonal of a parallelogram OACB, and then find the unit vector in the same direction.
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Use the fact that diagonals of a parallelogram bisect the interior angles.
This is only true for a rhombus.
The diagonals of a parallelogram will always bisect each other, but not necessarily the angles at which they meet.
Note that in the diagram below, it is not necessarily true that \(\angle ADE=\angle EDC\), but we do indeed have \(\overline{AE}=\overline{EC}\) for example.
(https://i.stack.imgur.com/SG59J.jpg)
The question first asked to find the unit vector of a and the unit vector of b.
This is precisely why the first part of the question asks you to find unit vectors in the direction of \(\vec{a}\) and \(\vec{b}\).
Once you have \(\hat{a}\) and \(\hat{b}\), you can proceed to use this property of a rhombus to answer the question.
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Thanks AlphaZero for correcting my error.