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# C4 Vector Question about the direction of a vector watch

1. Here's the solution to part c:
Attachment 703164703166

I get that for r=a+tb, you use the vector for M (5,1,5) since that is the point. Then you need b to be the directional vector.

I get that they can use l as the directional vector because OL is parallel to LM. However, OL is going vertically diagonally whereas MN is going vertically downwards, so doesn't the position vector l need to be made negative to represent MN? (because although OL is parallel to LM, they're in opposite directions). If it doesn't need to be made negative and the mark scheme is correct, why don't you need to make it negative?

Surely if OL was the directional vector to go upwards from O to L, then using the same directional vector from M would make you go upwards from M rather than downwards towards N? Can you explain please?

Thanks a lot!
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2. (Original post by vector12)
I get that for r=a+tb, you use the vector for M (5,1,5) since that is the point. Then you need b to be the directional vector.

I get that they can use l as the directional vector because OL is parallel to LM. However, OL is going vertically diagonally whereas MN is going vertically downwards, so doesn't the position vector l need to be made negative to represent MN? (because although OL is parallel to LM, they're in opposite directions). If it doesn't need to be made negative and the mark scheme is correct, why don't you need to make it negative?

Surely if OL was the directional vector to go upwards from O to L, then using the same directional vector from M would make you go upwards from M rather than downwards towards N? Can you explain please?

Thanks a lot!
r = p + tq

In the vector equation, t is a scalar that could be positive or negative. So as long as q is parallel to the line, you can use it as your direction vector. You could also use any other vector parallel to the line e.g.

r = p + t(-2q)

t can be any scalar so this also works.

I think this is what you are talking about but let us know if you're still unsure.
3. (Original post by Notnek)
r = p + tq

In the vector equation, t is a scalar that could be positive or negative. So as long as q is parallel to the line, you can use it as your direction vector. You could also use any other vector parallel to the line e.g.

r = p + t(-2q)

t can be any scalar so this also works.

I think this is what you are talking about but let us know if you're still unsure.
That's kind of what I was asking about. For the vector OL, which is the directional vector l, (2,-2,3), the direction of that vector is going from the origin towards L, which is going upwards (let's say in the positive Y direction). However, MN is parallel to OL, so you can use that directional vector.

But the directional vector for MN should be going in the negative Y direction to get from M to N, whereas they can still use the directional vector l, or OL, which is going in the positive Y direction instead. How come that is? Using that same directional vector would suggest that you go in the vertical Y direction upwards from M, would it not, rather than going downwards?
4. (Original post by vector12)
That's kind of what I was asking about. For the vector OL, which is the directional vector l, (2,-2,3), the direction of that vector is going from the origin towards L, which is going upwards (let's say in the positive Y direction). However, MN is parallel to OL, so you can use that directional vector.

But the directional vector for MN should be going in the negative Y direction to get from M to N, whereas they can still use the directional vector l, or OL, which is going in the positive Y direction instead. How come that is? Using that same directional vector would suggest that you go in the vertical Y direction upwards from M, would it not, rather than going downwards?
Maybe I'm misunderstanding your question but you seem confused about what the vector equation of a line is and where it coms from.

In this question you're finding the vector equation of the line MN. This is a line not a vector so you could also call this the line NM - it doesn't matter. As I said above, in the vector equation of a line, the direction vector is any vector parallel to the line, it can be in any direction.

It may be worth watching this video to understand what the vector equation of a line means and how it is formed.

If you understand all this and agree with my post but are still stuck then please try clarifying your question again.
5. (Original post by vector12)
That's kind of what I was asking about. For the vector OL, which is the directional vector l, (2,-2,3), the direction of that vector is going from the origin towards L, which is going upwards (let's say in the positive Y direction). However, MN is parallel to OL, so you can use that directional vector.

But the directional vector for MN should be going in the negative Y direction to get from M to N, whereas they can still use the directional vector l, or OL, which is going in the positive Y direction instead. How come that is? Using that same directional vector would suggest that you go in the vertical Y direction upwards from M, would it not, rather than going downwards?
Do you agree that ?

So your eq. for is just as you'd say, correct?

But note that this is just the same as

Since can be any number in , we can just get rid off the negative (as it doesn't really matter) by saying that , and say that:

as the question has it, almost.

(Of course, as the negative doesnt really matter, we can just ignore it and leave the last line here with rather than , just as the question shows)
6. (Original post by RDKGames)
Do you agree that ?

So your eq. for is just as you'd say, correct?

But note that this is just the same as

Since can be any number in , we can just get rid off the negative (as it doesn't really matter) by saying that , and say that:

as the question has it, almost.

(Of course, as the negative doesnt really matter, we can just ignore it and leave the last line here with rather than , just as the question shows)
Ah, okay. I understand what you've done. So in reality, it's the t that is positive or negative (and any real number) and if it were positive, it would mean it was going in the opposite direction to if t were negative? Is that right?
7. (Original post by vector12)
Ah, okay. I understand what you've done. So in reality, it's the t that is positive or negative (and any real number) and if it were positive, it would mean it was going in the opposite direction to if t were negative? Is that right?
Yes in reality it doesn't matter because we allow . Not sure what you ask in the second part there.

It basically boils down to: if my directional vector goes the opposite way (like OL goes opposite MN), well it doesn't matter, just pick appropriate in the equation and you'll set it going in the correct direction again. The only thing that matters here is that the directional vector you pick MUST be parallel to your wanted dir. vector.

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