Vector Co-ordinates

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In summary, Homework Equations asks you to find the distance and direction from a starting point using co-ordinate vectors. The Attempt at a Solution reads that you can find the distance by drawing two right angle triangles and adding it via vector laws.
  • #1
geoff18
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Homework Statement


A car travels 3km due North then 5km North East. Use co-ordinate vectors to find the distance and direction from the starting point.


Homework 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 don't think that is what the question wants.


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
 
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  • #2
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
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
geoff18 said:
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?

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
azizlwl said:
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.


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
Yes, the "northeast" direction is at 45 degrees to both "north" and "east" so the two components are equal. So [itex]a^2+ b^2= a^2+ a^2= 5^2[/itex].
 
  • #7
geoff18 said:
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

Yes, maybe with a help of a diagram can make it easier for you find the answers.
 
  • #8
so the co-ordinate of the third point will be ((sqrt of 25)/2)),((sqrt of 25)/2))+3))
 
  • #9
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
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)?

The answer states: 7.43 tho?

Did I do something wrong?
 
Last edited:
  • #11
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:
  • #12
Hi Thanks for the picture azizlwl, so using tri functions, i assume that the point will be:
(5cos(45), ((5*sin(45))+3))
 
  • #13
geoff18 said:
Hi Thanks for the picture azizlwl, so using tri functions, i assume that the point will be:
(5cos(45), ((5*sin(45))+3))

Correct.
 
  • #14
geoff18 said:
Hi Thanks for the picture azizlwl, so using tri functions, i assume that the point will be:
(5cos(45), ((5*sin(45))+3))

attachment.php?attachmentid=47862&stc=1&d=1338481322.png

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

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

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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1. What are vector coordinates?

Vector coordinates are a set of numerical values that describe the position, direction, and magnitude of a vector in a particular coordinate system.

2. How do you represent vector coordinates?

Vector coordinates are typically represented using an ordered set of values, such as (x, y, z), where each value represents the position of the vector along a specific axis in three-dimensional space.

3. What is the difference between vector coordinates and scalar coordinates?

Vector coordinates describe the position and direction of a vector, while scalar coordinates only describe the position of a point in space. In other words, vector coordinates have both magnitude and direction, while scalar coordinates only have magnitude.

4. How are vector coordinates used in mathematics and science?

Vector coordinates are used to describe and analyze physical quantities such as velocity, force, and acceleration in mathematics and science. They are also essential in fields such as physics, engineering, and computer graphics.

5. Can vector coordinates be represented in different coordinate systems?

Yes, vector coordinates can be represented in different coordinate systems, such as Cartesian, polar, and spherical coordinates. Each coordinate system has its own set of rules for determining the vector coordinates, but the values will ultimately describe the same vector in space.

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