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Collinear vector help

  • Thread starter omicron
  • Start date
The position vectors of A, B and C relative to an origin O are [tex]-I+pj[/tex], [tex]5i+9j[/tex] & [tex]6i+8j[/tex] respectively. Determine the value of p for which A, B & C are collinear.
 
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Have you learned any coordinate geometry at school?
 
Yes I have.
 
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So you may instead assign the coordinates (-1,p) to the position vector -i + pj, (5,9) to the position vector 5i + 9j and (6,8) to the position vector 6i + 8j.

If three points are collinear, this means that the gradient between any two points of the three is the same.
 
Thank you!
 
One more question.
a) The vector [tex]\displaystyle \overrightarrow{OA}[/tex] has magnitude 100 and has the same direction as [tex]\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)[/tex]. Express [tex]\displaystyle \overrightarrow{OA}[/tex] as a column vector.
b) The vector [tex]\displaystyle \overrightarrow{OB}[/tex] is [tex]\displaystyle \left(\begin{array}{cc}24\\99\end{array}\right)[/tex]. Obtain the unit vector in the direction of [tex]\displaystyle \overrightarrow{AB}[/tex].
 
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omicron said:
One more question.
a) The vector [tex]\displaystyle \overrightarrow{OA}[/tex] has magnitude 100 and has the same direction as [tex]\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)[/tex]. Express [tex]\displaystyle \overrightarrow{OA}[/tex] as a column vector.
b) The vector [tex]\displaystyle \overrightarrow{OB}[/tex] is [tex]\displaystyle \left(\begin{array}{cc}24\\99\end{array}\right)[/tex]. Obtain the unit vector in the direction of [tex]\displaystyle \overrightarrow{AB}[/tex].
You need to show evidence of some work. Do you know what unit vectors are?
 
Yes I do know.
 
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Then you should be able to solve both of those problems..
 
If I did, I wouldn't have posted them. :bugeye:
 
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omicron said:
One more question.
a) The vector [tex]\displaystyle \overrightarrow{OA}[/tex] has magnitude 100 and has the same direction as [tex]\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)[/tex]. Express [tex]\displaystyle \overrightarrow{OA}[/tex] as a column vector.
First of all, find the magnitude of the vector [tex]\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)[/tex]. What is it?

b) The vector [tex]\displaystyle \overrightarrow{OB}[/tex] is [tex]\displaystyle \left(\begin{array}{cc}24\\99\end{array}\right)[/tex]. Obtain the unit vector in the direction of [tex]\displaystyle \overrightarrow{AB}[/tex].
Do you know how to calculate the vector [tex]\displaystyle \overrightarrow{AB}[/tex]? (Hint: use information from a)
 

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