Finding p so that A, B and C are collinear

[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.

 

[recon]

Have you learned any coordinate geometry at school?

 

[omicron]

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.

 

[omicron]

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]

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?

 

[omicron]

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.

 

[recon]

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)