I with this question about vectors

[LCKurtz]

How's that? Not good. You haven't even used $t$.

If you had actually read and responded to my posts you would have had this problem solved a week ago. You haven't simplified your answer in post #25 or responded to post #28. Until you do you will hear nothing more from me.

 

[lioric]

How's that? Not good. You haven't even used $t$.

If you had actually read and responded to my posts you would have had this problem solved a week ago. You haven't simplified your answer in post #25 or responded to post #28. Until you do you will hear nothing more from me.

I'm sorry about that
Was away for some time and no internet there
But I'll start working on this now.
Ok so simplifying the new position of P
(1+5t)i + (7+5t)j
P= i+5ti + 7j+5tj
New position of Q
(3+6t)i + (5t-8)j
Q= 3i+6ti + 5tj-8j

Q-P
(3i-8j)-(i+7j)
=(2i-15j)

 

[LCKurtz]

Make sure you are using the correct numbers as given in post #18.
When you "simplify" a vector it should look like (...)i + (...)j, one i term and one j term.
Your final answer for Q-P at time t must have a "t" in it.
Then we can talk about whether it points NE.

 

[lioric]

Post 18

At noon two boats P and Q have a position vector (i+7j)km and (3i-8j)km respectively to the origin O. i and j are unit vectors in direction to East and north respectively P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h

 

[lioric]

Make sure you are using the correct numbers as given in post #18.
When you "simplify" a vector it should look like (...)i + (...)j, one i term and one j term.
Your final answer for Q-P at time t must have a "t" in it.
Then we can talk about whether it points NE.

I m very confused
In post #25 it seems that the vectors are in the format that you asked (...)i+(...)j and you asked me to simply them. So I expanded them and now your asking me to revert them back again.

 

[lioric]

Are you asking me to subtract the new coordinates of P and Q or the initial coordinates given in the question?

 

[LCKurtz]

I m very confused
In post #25 it seems that the vectors are in the format that you asked (...)i+(...)j and you asked me to simply them. So I expanded them and now your asking me to revert them back again.

OK, never mind about the i and j comments.
This thread is getting very jumbled. There are multiple arithmetic errors and/or typos. In post #25 you have an arithmetic mistake in the new position of P. Then in post #32 you carried the same mistake through. Also in post #32 you dropped the $t$ in the calculation of Q-P, as I told you in post #33. Fix those. Once you finally get Q-P correct, with a $t$ in it, it is a simple one more step to finish your problem.

 

[lioric]

OK, never mind about the i and j comments.
This thread is getting very jumbled. There are multiple arithmetic errors and/or typos. In post #25 you have an arithmetic mistake in the new position of P. Then in post #32 you carried the same mistake through. Also in post #32 you dropped the $t$ in the calculation of Q-P, as I told you in post #33. Fix those. Once you finally get Q-P correct, with a $t$ in it, it is a simple one more step to finish your problem.

That's what I was clarifying in post 36
The initial P and Q position vectors given in the question has no t in it
So which P and Q are you referring to?
Is it the answers on post 25?

 

[LCKurtz]

That's what I was clarifying in post 36
The initial P and Q position vectors given in the question has no t in it
So which P and Q are you referring to?
Is it the answers on post 25?

Think about the problem you are trying to solve. You are given original positions P and Q and their velocities. They are moving. Then you are asked at what time $t$ is Q northeast of P. So you need their positions at time $t$ don't you? So you need to know for what $t$ does Q-P point northeast. Fix your arithmetic and show Q-P as a function of $t$ and you are almost done.

 

[lioric]

Think about the problem you are trying to solve. You are given original positions P and Q and their velocities. They are moving. Then you are asked at what time $t$ is Q northeast of P. So you need their positions at time $t$ don't you? So you need to know for what $t$ does Q-P point northeast. Fix your arithmetic and show Q-P as a function of $t$ and you are almost done.

Ok
Let's think here
I'm just trying to clear my confusion please do tell if I'm thinking right

Let's keep the vector situation and go to a simpler linear one
Let's say P is on (1,1) on a grid
And Q is on ( 5,-5) on the same grid
P is moving on positive x-axis (to the right) at let's say 1 unit/s
And Q is moving in the positive y-axis (upward) 1 unit/s
Let's say the question is asking to find the time that P moves east of Q

Is this the same or similar sort of thing?

 

[LCKurtz]

Ok
Let's think here
I'm just trying to clear my confusion please do tell if I'm thinking right

Let's keep the vector situation and go to a simpler linear one
Let's say P is on (1,1) on a grid
And Q is on ( 5,-5) on the same grid
P is moving on positive x-axis (to the right) at let's say 1 unit/s
And Q is moving in the positive y-axis (upward) 1 unit/s
Let's say the question is asking to find the time that P moves east of Q

Is this the same or similar sort of thing?

I am not going to go off on another tangent with you. You have understood the problem well enough to draw a picture long ago in post #19. Just finish the problem as I have suggested to you.

 

[lioric]

I am not going to go off on another tangent with you. You have understood the problem well enough to draw a picture long ago in post #19. Just finish the problem as I have suggested to you.

If I understood I wouldn't ask

But from what I have gathered and from the things you have asked me to do this is what I came up with
P initial position (i +7j) velocity (5i-5j)
Q initial position (3i-8j) velocity (6i+5j)

P new position
(i +7j)+(5i-5j)t.
(1+5t)i + (7-5t)j

Q new position
(3i-8j)+(6i+5j)t
(3+6t)i +(5t-8)j

Now Q-P

(3+6t)i + (5t-8)j - [ (1+5t)i + (7-5t)j ]
(3+6t)i + (5t-8)j - (1+5t)i - (7-5t)j
(3+6t)i + (5t-8)j +(-1-5t)i +(-7+5t)j
(3-1+6t-5t)i + (5t+5t-8-7)j
(2+t)i + (10t-15)j

Is this what you asked?

 

[LCKurtz]

Yes. Finally! Now, for what $t$ does that point northeast? What do you require about the components for a vector to point northeast?

 

[lioric]

Yes. Finally! Now, for what $t$ does that point northeast? What do you require about the components for a vector to point northeast?

It should point to somewhere in the first quadrant meaning it should not have a bearing exceeding 90 degrees

 

[LCKurtz]

I would assume in this problem that the meaning of northeast means exactly northeast, that is midway between north and east.

 

[lioric]

I would assume in this problem that the meaning of northeast means exactly northeast, that is midway between north and east.

So that means as I said before bearing of 45 degrees

 

[LCKurtz]

So that means as I said before bearing of 45 degrees

Yes. And the question asks at what time does that happen? So...

 

[lioric]

Yes. And the question asks at what time does that happen? So...

We have to find the time taken to make 45 degrees between P and Q
But I don't know how

 

[LCKurtz]

Do you know how to tell if any vector points NE? Which, if any, of the following vectors point NE?
3i - 5j
2i +3j
-i - 2j
3i + 3j
i - j
-2i + 2j
Explain how you can tell.

 

[lioric]

Do you know how to tell if any vector points NE? Which, if any, of the following vectors point NE?
3i - 5j
2i +3j
-i - 2j
3i + 3j
i - j
-2i + 2j
Explain how you can tell.

Ya the 3i+3j
It means the position is 3,3 on an x,y axis
The gradient of that would be 1 and that gives a 45 degrees

 

[LCKurtz]

OK. So what, if any, value of $t$ makes Q-P point NE? That answer is the solution to your problem. Although the problem may want to know what time of day is it, given it started at noon.

 

[lioric]

OK. So what, if any, value of $t$ makes Q-P point NE? That answer is the solution to your problem. Although the problem may want to know what time of day is it, given it started at noon.

Multiply by sin45?

 

[LCKurtz]

Multiply by sin45?

That answer makes no sense at all. You are asked for a value of $t$ and you reply "multiply by sin45".

 

[lioric]

That answer makes no sense at all. You are asked for a value of $t$ and you reply "multiply by sin45".

sorry
well in order to be 45 degrees Q has to have the same amount of x and y values away from P
eg: if Q if 3i away from Q it should also have 3j away from P
But you have to understand this that I'm trying but I don't know how to use this information to find a t value for this problem
I do understand that Q-P was to find the distance between P and Q at a certain time t
But I don't know how to find t when Q is 45 degrees to P
I'm just having this problem because I'm not used to doing vector type questions.
If it was simple distance and time I could cope.
So please lend me a hand
Thanks to you I can this far and I really appreciate it

 

[Mark44]

From post #42:

Now Q-P

(2+t)i + (10t-15)j

From post #43:

Yes. Finally! Now, for what t does that point northeast? What do you require about the components for a vector to point northeast?

What relationship has to exist between the i and j coordinates for a vector to point northeast?

 

[lioric]

From post #42:From post #43:

What relationship has to exist between the i and j coordinates for a vector to point northeast?

They have to be positive and same magnitude

 

[LCKurtz]

They have to be positive and same magnitude

You could have answered that way back when I asked it in post #43.

So, what value of $t$, if any, makes that happen for Q-P?

 

[Mark44]

From post #42:

Now Q-P
.
.
.
(2+t)i + (10t-15)j

What relationship has to exist between the i and j coordinates for a vector to point northeast?

They have to be positive and same magnitude

So what do you get?

 

[lioric]

From post #42:So what do you get?

Ok I get what your saying
As I mentioned before I'm having such a hard time due to vector with i & j form
I know if it's pointing to NE the values have to be positive and same
I just don't know how to change it or in other words the proper way to do the sum when it comes to vectors
I'm not clear about the "protocol " to change the i and j in relation with time

 

[LCKurtz]

Put $t=1$ in your vector. Does it point NE? How about $t = 2$ or $t=3$ etc. The question is, is there any value of $t$ that gives a vector that points NE.