# Collinear vector help

#### omicron

The position vectors of A, B and C relative to an origin O are $$-I+pj$$, $$5i+9j$$ & $$6i+8j$$ respectively. Determine the value of p for which A, B & C are collinear.

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#### recon

Have you learned any coordinate geometry at school?

Yes I have.

#### recon

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!

#### omicron

One more question.
a) The vector $$\displaystyle \overrightarrow{OA}$$ has magnitude 100 and has the same direction as $$\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)$$. Express $$\displaystyle \overrightarrow{OA}$$ as a column vector.
b) The vector $$\displaystyle \overrightarrow{OB}$$ is $$\displaystyle \left(\begin{array}{cc}24\\99\end{array}\right)$$. Obtain the unit vector in the direction of $$\displaystyle \overrightarrow{AB}$$.

#### Nylex

omicron said:
One more question.
a) The vector $$\displaystyle \overrightarrow{OA}$$ has magnitude 100 and has the same direction as $$\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)$$. Express $$\displaystyle \overrightarrow{OA}$$ as a column vector.
b) The vector $$\displaystyle \overrightarrow{OB}$$ is $$\displaystyle \left(\begin{array}{cc}24\\99\end{array}\right)$$. Obtain the unit vector in the direction of $$\displaystyle \overrightarrow{AB}$$.
You need to show evidence of some work. Do you know what unit vectors are?

Yes I do know.

#### Nylex

Then you should be able to solve both of those problems..

#### omicron

If I did, I wouldn't have posted them. Last edited:

#### recon

omicron said:
One more question.
a) The vector $$\displaystyle \overrightarrow{OA}$$ has magnitude 100 and has the same direction as $$\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)$$. Express $$\displaystyle \overrightarrow{OA}$$ as a column vector.
First of all, find the magnitude of the vector $$\displaystyle \left(\begin{array}{cc}7\\24\end{array}\right)$$. What is it?

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

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