Need finding my way home! (vectors and matrices)

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Denzel

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So 13. (c) Do I go further or is that it? Should I just say that because RS is a factor of RM therefor it is parallel? Or are there more steps I should take?1.png1554293794633.png1554293808069.png
 
Denzel said:
So 13. (c) Do I go further or is that it? Should I just say that because RS is a factor of RM therefor it is parallel? Or are there more steps I should take?
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I'm not even sure what it means to say a segment (or vector?) is a factor of another, or what RM has to do with a question about RS and KL.

I would just write expressions for RS and KL and show that one is a scalar multiple of the other.

It's hard to read your work, but I don't see that you've said anything about KL at all.
 
Sorry that my writing is hard to understand.. This is what I worked out. I do not understand1554570030088.png how to prove that they are parallel though.
 
You have expressed the vectors in terms of k and s, by which you apparently mean OS = 1/3 m; they haven't defined that. I used the given k and m instead.

But in RS, you used 1/3 s where you should have had s, or 1/3 m. Your KL also is not quite correct; write out a couple more steps in your work so you can check it more easily.

Make those corrections, and then express all the fractions in each of KL and RS using a common denominator. That will make the fact you need to show clearer.
 
I tried this. I don't seem to find any way to even out the denominators.
11703
 
You have
KL = -5/4 k + 1/2 m​
RS = -1/2 k + 1/3 m​

Write each of these using a common denominator, and factor out a fraction to see if they are parallel:
KL = -5/4 k + 2/4 m = (1/4)(-5 k + 2 m)​
RS = -3/6 k + 2/6 m = (1/6)(-3 k + 2 m)​

Clearly they are not parallel, if your work is correct, so go back and check. I'd suggest focusing on KL, the more complicated one, and write more steps, as I said before. It appears that you are thinking KL = -OK + OL, and OK = k while OL = -1/4 k + 1/2 m. But what is OL, really?
 
Some crucial parts are too faint to be sure of, but your KL at least is still wrong. (I think RS is right.) You still aren't showing enough steps for me to tell where you are going wrong.
 
I hope you don't run out of patience with me. 1554905273364.png I love having to work for something I want! Is this working wrong?
 
Some of this makes no sense to me, especially the second line. L is not a vector, and RM is not PO + OL. And your result for KL is just a little off as a result.

Here's how I might start:

KL = KO + OL​
= KO + OR + RL​
= KO + OR + 1/2 RM​
= KO + OR + 1/2(RO + OM)​

Now put in the names k and m appropriately, and see what you get. As I said, because there is a lot going on here, we need to write down the details in a way we can check before going on. (I made a mistake or two in this before getting it right, because I was trying to do it all in my head - not a good idea!)
 
Dr.Peterson said:
Some of this makes no sense to me, especially the second line. L is not a vector, and RM is not PO + OL. And your result for KL is just a little off as a result.

Here's how I might start:

KL = KO + OL​
= KO + OR + RL​
= KO + OR + 1/2 RM​
= KO + OR + 1/2(RO + OM)​

Now put in the names k and m appropriately, and see what you get. As I said, because there is a lot going on here, we need to write down the details in a way we can check before going on. (I made a mistake or two in this before getting it right, because I was trying to do it all in my head - not a good idea!)
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I don't understand what OR→ is... or rather, why is it there?
 
Denzel said:
I don't understand what OR→ is... or rather, why is it there?
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Do you understand now, since you got the correct answer?

We need OR in order to find OL, based on its definition. There may well be several other ways to do this, though.

In your final answer, you should have some parentheses that you omitted, but you did what I did. Both are multiples of -3k + 2m, so they are parallel.
 
Dr.Peterson said:
Do you understand now, since you got the correct answer?

We need OR in order to find OL, based on its definition. There may well be several other ways to do this, though.

In your final answer, you should have some parentheses that you omitted, but you did what I did. Both are multiples of -3k + 2m, so they are parallel.
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I actually still don't understand the concept behind OR... v_v
 
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OR is the vector from O to R. What is it that you don't understand?

Is it not clear that OL = OR + RL? (I just noticed that when you copied my work, you wrote OR in place of KO on the first line, which would indeed be confusing if it were what I wrote.)
 
I thought that KL→ was k and the midpoint of RM being 1/2 RO→+OM→ How do we get the OR in the middle? KO + →(OR)<-- + 1/2(RO + OM)
 
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They state right in the problem that OK = k.

The midpoint of segment RM is the point L. Its position vector is OL, and is the average of position vectors OR and OM.

RO + OM is the vector RM; half of that is the vector RL.

I think you may be confusing points and vectors.
 
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