# Homework Help: Vector Co-ordinates

1. May 30, 2012

### geoff18

1. The problem statement, all variables and given/known data
A car travels 3km due North then 5km North East. Use co-ordinate vectors to find the distance and direction from the starting point.

2. Relevant equations
I understand that co-ordinate vectors meant the column vector, but I don't understand how to convert the above description into vectors. I can calculate the distance by drawing two right angle triangles find the sides and addition it via vector laws and pythag theorm. But I dont think that is what the question wants.

3. The attempt at a solution
I read thru my lecture notes and attempt to google the answers but most of the results just explain using a1=|a|*cos(a) etc

2. May 30, 2012

### cupid.callin

Assume the starting position of car as origin. You can plot the coordinates of two points that are being talked about in ques. ( first where car changes direction and second where car is finally.

The vector between any two points A(a,b) and B(c,d) is given as,
Vec(BA) = (c-a)i + (d-b)j

Find two vectors and then add them to get net vector.
The you can find its magnitude

3. May 30, 2012

### geoff18

Hi thanks for the prompt reply, rly appreciate it.

so origin would be (0,0)
Second point would be (0,3)
Third Point would be (5/root2, 3+(5/root2))
?

If that is the case, wouldn't the effort to find those co-ordinates already solve the length of the distance?

4. May 30, 2012

### azizlwl

Second point you move up vertically 3 units, so pt.(0,3) correct.
Then you move another 5 units in North east direction, so the pt is (?,?)

The question is how many units are there from (0,0) to (?,?) and direction.

5. May 30, 2012

### geoff18

Hi Azizlwl, thanks for the reply.
How would I write the co-ordinates of 5 units moving in north east direction?
Would i need to use pythag's theorm to calculate the co-ordinates?
thanks

6. May 30, 2012

### HallsofIvy

Yes, the "northeast" direction is at 45 degrees to both "north" and "east" so the two components are equal. So $a^2+ b^2= a^2+ a^2= 5^2$.

7. May 30, 2012

### azizlwl

Yes, maybe with a help of a diagram can make it easier for you find the answers.

8. May 30, 2012

### geoff18

so the co-ordinate of the third point will be ((sqrt of 25)/2)),((sqrt of 25)/2))+3))

9. May 30, 2012

### azizlwl

Let me rephase again.
You move up 3 units vertically from origin (0,0) to points (0,3) equal to 3 units north.
From point (0,3) you move another 5 units in direction of northeast.
This property of movement is called vector since it has units(magnitude) and direction too.

Northeast means equal north and east.
Direction of northeast means if you move "b" units to north, you have to move another "b" units to the east too.
Now you have moved not only in direction of north but also in direction of east.

Now try to draw the diagram.Later you will be able to draw on you mind without resorting to paper.

10. May 30, 2012

### geoff18

so according to this then:
Origin: (0,0)
First point: (0,3)
Second Point: (5,8) [Moved move 5 units right/east AND 5 units up/north]

so the distance should be 5^2+8^2=25+64=89
=sqrt(89) =>9.43(approx)?

Did I do something wrong?

Last edited: May 30, 2012
11. May 30, 2012

### azizlwl

1st pt=(0,0)
2nd. pt=(0,3)
3rd pt =(?,?) NOT (5,8)

Use phytagoras theorem or trig. function find 3rd point.

http://img521.imageshack.us/img521/2084/p1010011wx.jpg [Broken]

Last edited by a moderator: May 6, 2017
12. May 31, 2012

### geoff18

Hi Thanks for the picture azizlwl, so using tri functions, i assume that the point will be:
(5cos(45), ((5*sin(45))+3))

13. May 31, 2012

### azizlwl

Correct.

14. May 31, 2012

### cupid.callin

Hi geoff18 ...
So now you have found all the three points as shown above. Now you can find the Vectors BA and CB as i told you before

But what I am not sure is how you are supposed to proceed now ...
There are two (common) ways to proceed now,
I. Find BA, CB and then find BA using vector addition law.
II. Directly find CA using points C and A

Anyone would use II method but as i am unaware of what you are supposed to do, i will and must leave that decision for you :D

EDIT: C will be (3 + 5 sin 45)

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