Grade 12 - Matrices and Vectors - Need help

L

laoch

New member
Joined
Sep 11, 2008
Messages
4
The problem reads:

The points P, Q and R are such that QR = 4PQ. ( arrow above)
Given that the position vectors of P and Q relative to an origin O are
( 6 )
( 7 )
and
( 9 )
( 20 )
respectively, find the unit vector parallel to OR( arrow above)
 
laoch said:
The problem reads:

The points P, Q and R are such that QR = 4PQ. ( arrow above)
Given that the position vectors of P and Q relative to an origin O are
( 6 )
( 7 )
and
( 9 )
( 20 )
respectively, find the unit vector parallel to OR( arrow above)
Click to expand...

Please share with us your work/thoughts - so that we know where to begin to help.

Start with drawing a sketch of the vectors and the points.

Can you tell us - what does QR = 4 PQ mean in vector terms?
 
I drew a graph and plotted two straight lines each originating from O.

PQ =
( 6 )
( 20 )

Unfortunately I don't understand the question entirely. I don't know how to find R.

QR = 4 PQ ( -> arrow line above the QR and PQ)
 
laoch said:
I drew a graph and plotted two straight lines each originating from O.

PQ =
( 6 )
( 20 )

This is not correct

If you have two points A(x[sub:3edu2k0p]a[/sub:3edu2k0p],y[sub:3edu2k0p]a[/sub:3edu2k0p]) and B(x[sub:3edu2k0p]b[/sub:3edu2k0p],y[sub:3edu2k0p]b[/sub:3edu2k0p])

Then vector AB is

AB = (x[sub:3edu2k0p]b[/sub:3edu2k0p] - x[sub:3edu2k0p]a[/sub:3edu2k0p])i + (y[sub:3edu2k0p]b[/sub:3edu2k0p] - y[sub:3edu2k0p]a[/sub:3edu2k0p])j

You need to understand this part thoroughly before you can do rest of the problem.



Unfortunately I don't understand the question entirely. I don't know how to find R.

QR = 4 PQ ( -> arrow line above the QR and PQ)
Click to expand...

QR = 4 PQ

In vector terms it means that

the magnitude of Vector QR is 4 times that of the vector PQ

and

Vector QR and vector PQ are in the same direction (i.e. unit vector along QR - expressed as e[sub:3edu2k0p]QR[/sub:3edu2k0p] and unit vector along PQ - expressed as e[sub:3edu2k0p]PQ[/sub:3edu2k0p] are same)

Graphically it will mean that - if you extend the line joining PQ - The point R will be on that line and

length of line QR = 4 times (length of line PQ)

So now express PQ vectorially - and find its magnitude and direction (unit vector) - then define vector QR - determine the position vector OR
 
Subhotosh Khan said:
laoch said:
I drew a graph and plotted two straight lines each originating from O.

PQ =
( 6 )
( 20 )

This is not correct

If you have two points A(x[sub:25p7bxyd]a[/sub:25p7bxyd],y[sub:25p7bxyd]a[/sub:25p7bxyd]) and B(x[sub:25p7bxyd]b[/sub:25p7bxyd],y[sub:25p7bxyd]b[/sub:25p7bxyd])

Then vector AB is

AB = (x[sub:25p7bxyd]b[/sub:25p7bxyd] - x[sub:25p7bxyd]a[/sub:25p7bxyd])i + (y[sub:25p7bxyd]b[/sub:25p7bxyd] - y[sub:25p7bxyd]a[/sub:25p7bxyd])j

You need to understand this part thoroughly before you can do rest of the problem.



Unfortunately I don't understand the question entirely. I don't know how to find R.

QR = 4 PQ ( -> arrow line above the QR and PQ)
Click to expand...

QR = 4 PQ

In vector terms it means that

the magnitude of Vector QR is 4 times that of the vector PQ

and

Vector QR and vector PQ are in the same direction (i.e. unit vector along QR - expressed as e[sub:25p7bxyd]QR[/sub:25p7bxyd] and unit vector along PQ - expressed as e[sub:25p7bxyd]PQ[/sub:25p7bxyd] are same)

Graphically it will mean that - if you extend the line joining PQ - The point R will be on that line and

length of line QR = 4 times (length of line PQ)

So now express PQ vectorially - and find its magnitude and direction (unit vector) - then define vector QR - determine the position vector OR
Click to expand...

Firstly, I'd like to thank you so much for your help. I've been struggling with this question for days - it really means a lot. :)

I understand the last part fully, but could you explain AB = (x[sub:25p7bxyd]b[/sub:25p7bxyd] - x[sub:25p7bxyd]a[/sub:25p7bxyd])i + (y[sub:25p7bxyd]b[/sub:25p7bxyd] - y[sub:25p7bxyd]a[/sub:25p7bxyd])j?
Where does i and j come from? You are right -"You need to understand this part thoroughly before you can do rest of the problem.".
I'm not sure how I could substitute this entire equation?

Thanks again, sorry for all the confusion lol
 
[quote="laoch

I understand the last part fully, but could you explain AB = (x[sub:2f34gfs8]b[/sub:2f34gfs8] - x[sub:2f34gfs8]a[/sub:2f34gfs8])i + (y[sub:2f34gfs8]b[/sub:2f34gfs8] - y[sub:2f34gfs8]a[/sub:2f34gfs8])j?

Where does i and j come from?

In cartesian co-ordinate system - how do express a vector?

How do you express unit vectors along x-axis and y-axis

Thanks again, sorry for all the confusion lol[/quote]
 
Ok. My book doesn't share any relevant information towards unit vectors, ironically.

As far as I understand, i and j would be the magnitude of P and Q, correct?

I would substitute the x co-ordinates in for (xb - xa) and y co-ordinates for (yb - ya)?
 
You must log in or register to reply here.
Top