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March 29, 2024, 04:20:08 am

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164303 times)  Share 

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generalkorn12

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Re: Specialist 3/4 Question Thread!
« Reply #645 on: September 01, 2012, 11:30:36 am »
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For a question such as, |v|=(13-12sin(t))1/2, why is that when |v|=-1, there is a maximum? From the sin graph i can only see +1 as when the graph is a maximum.

Also, are vectors parallel if they're scalar multiples of eachother, regardless of the signs the i, j or k's carry?
« Last Edit: September 01, 2012, 11:50:12 am by generalkorn12 »

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #646 on: September 01, 2012, 03:55:52 pm »
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For a question such as, |v|=(13-12sin(t))1/2, why is that when |v|=-1, there is a maximum? From the sin graph i can only see +1 as when the graph is a maximum.

Also, are vectors parallel if they're scalar multiples of eachother, regardless of the signs the i, j or k's carry?

|v| cant be equal a negative number, maybe they mean v=-1?

Vectors are not parallel if they're scalar multiples of each other, regardless of i,j,k
For example:
a= 2i+j+k => |a|=sqr(6)
b=2sqr(5)i+sqr(2)j+sqr(2)k => |b|=2sqr(6)

|b|=2|a| but vector a is not parallel to vector b

Btw, does anyone know how to type vectors and signs of i,j,k in LaTex? Thanks!




paulsterio

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Re: Specialist 3/4 Question Thread!
« Reply #647 on: September 01, 2012, 04:12:33 pm »
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Vectors are not parallel if they're scalar multiples of each other, regardless of i,j,k

Yes they are, the whole definition of parallel is that a is // to b if a = kb where k is a real constant.

Also, are vectors parallel if they're scalar multiples of eachother, regardless of the signs the i, j or k's carry?

only if the signs are the same or opposite. For example, 2i + 2j is parallel to 10i + 10j. We agree on that. The value of k is 5. If the value of k was -5, then 2i + 2j would be parallel to -10i - 10j, in this case, they are all opposite. However, 2i + 2j would not be parallel to 10i - 10j or -10i + 10j.

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #648 on: September 01, 2012, 04:26:14 pm »
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Vectors are not parallel if they're scalar multiples of each other, regardless of i,j,k

Yes they are, the whole definition of parallel is that a is // to b if a = kb where k is a real constant.


They are parallel if vector a=k*vector b. From there, you can say their scalar multiples each other

But you cant prove 2 vectors parallel just because their scalar multiples each other

Lasercookie

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Re: Specialist 3/4 Question Thread!
« Reply #649 on: September 01, 2012, 05:30:46 pm »
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They are parallel if vector a=k*vector b. From there, you can say their scalar multiples each other

But you cant prove 2 vectors parallel just because their scalar multiples each other
For parallel vectors, is true. This is what it means for a vector to be a scalar multiple of another.

Your statement is a bit contradictory, you seem to be saying that they are parallel if , but you can't prove them parallel if they are That doesn't really make much sense to me.

Note that does imply that for when k is greater than 0. being true doesn't imply that they're parallel vectors. The example you gave in your previous post is an example of this. I think that's what you're getting at, and I think the confusion is whether we're talking about the vectors a and b, or if we're talking about the magnitudes of vectors a and b.

For parallel vectors, we are talking about the vectors.
« Last Edit: September 01, 2012, 05:33:07 pm by laseredd »

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #650 on: September 01, 2012, 05:59:02 pm »
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They are parallel if vector a=k*vector b. From there, you can say their scalar multiples each other

But you cant prove 2 vectors parallel just because their scalar multiples each other
For parallel vectors, is true. This is what it means for a vector to be a scalar multiple of another.

Your statement is a bit contradictory, you seem to be saying that they are parallel if , but you can't prove them parallel if they are That doesn't really make much sense to me.

Note that does imply that for when k is greater than 0. being true doesn't imply that they're parallel vectors. The example you gave in your previous post is an example of this. I think that's what you're getting at, and I think the confusion is whether we're talking about the vectors a and b, or if we're talking about the magnitudes of vectors a and b.

For parallel vectors, we are talking about the vectors.

Yeah, I was talking about multiplies of magnitudes

If generalkorn meant scalar multiplies of vectors, if k is positive => they are parallel. If k is negative => they are anti-parallel

studynotes

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Re: Specialist 3/4 Question Thread!
« Reply #651 on: September 01, 2012, 06:20:33 pm »
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can i please have help with this definite integral

0 to pi/4 tan^3(x) dx

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #652 on: September 01, 2012, 06:38:35 pm »
+1
can i please have help with this definite integral

0 to pi/4 tan^3(x) dx



Let tan(x)=u, find

Afterthat you integrate function of u

You can do it by yourself then.


paulsterio

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Re: Specialist 3/4 Question Thread!
« Reply #653 on: September 01, 2012, 06:57:07 pm »
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But you cant prove 2 vectors parallel just because their scalar multiples each other

That's the only way to prove that 2 vectors are parallel, that they are scalar multiples of eachother. If you're saying that you CAN'T prove 2 vectors are parallel to eachother by this method then how do you show that 2 vectors are parallel?

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #654 on: September 01, 2012, 07:41:20 pm »
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But you cant prove 2 vectors parallel just because their scalar multiples each other

That's the only way to prove that 2 vectors are parallel, that they are scalar multiples of eachother. If you're saying that you CAN'T prove 2 vectors are parallel to eachother by this method then how do you show that 2 vectors are parallel?


They are parallel if vector a=k*vector b. From there, you can say their scalar multiples each other

But you cant prove 2 vectors parallel just because their scalar multiples each other
For parallel vectors, is true. This is what it means for a vector to be a scalar multiple of another.

Your statement is a bit contradictory, you seem to be saying that they are parallel if , but you can't prove them parallel if they are That doesn't really make much sense to me.

Note that does imply that for when k is greater than 0. being true doesn't imply that they're parallel vectors. The example you gave in your previous post is an example of this. I think that's what you're getting at, and I think the confusion is whether we're talking about the vectors a and b, or if we're talking about the magnitudes of vectors a and b.

For parallel vectors, we are talking about the vectors.

Yeah, I was talking about multiplies of magnitudes

If generalkorn meant scalar multiplies of vectors, if k is positive => they are parallel. If k is negative => they are anti-parallel

Lasercookie

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Re: Specialist 3/4 Question Thread!
« Reply #655 on: September 01, 2012, 07:53:46 pm »
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If generalkorn meant scalar multiplies of vectors, if k is positive => they are parallel. If k is negative => they are anti-parallel
I think this is just coming down to a matter of slightly different definitions and terminology really.

I would define parallel as "The non-zero vectors u and v are said to be parallel if there exists k ∈ R\{0} such that u = kv" (quoted from essentials) or in other words "Two vectors are parallel if they have the same direction or are in exactly opposite directions." (quoted from http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx)

Going by that definition, "anti-parallel" vectors are just parallel vectors that are in the opposite direction (http://en.wikipedia.org/wiki/Antiparallel_(mathematics)#Antiparallel_vectors). You also see the terminology "like parallel vectors" (facing the same direction) and "unlike parallel vectors" (facing the opposite direction) being used to refer to the same thing. 

I did a bit of searching but I can't really find a source that doesn't consider those vectors that face in the opposite direction to not be parallel.

That might not make sense if you're defining parallel vectors as only being scalar multiples that face that same direction - but going by most sources it seems the definition of a parallel vector is that it would be scalar multiples that have the same or opposite direction (in other words just .

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #656 on: September 01, 2012, 08:06:21 pm »
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If generalkorn meant scalar multiplies of vectors, if k is positive => they are parallel. If k is negative => they are anti-parallel
I think this is just coming down to a matter of slightly different definitions and terminology really.

I would define parallel as "The non-zero vectors u and v are said to be parallel if there exists k ∈ R\{0} such that u = kv" (quoted from essentials) or in other words "Two vectors are parallel if they have the same direction or are in exactly opposite directions." (quoted from http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx)

Going by that definition, "anti-parallel" vectors are just parallel vectors that are in the opposite direction (http://en.wikipedia.org/wiki/Antiparallel_(mathematics)#Antiparallel_vectors). You also see the terminology "like parallel vectors" (facing the same direction) and "unlike parallel vectors" (facing the opposite direction) being used to refer to the same thing. 

I did a bit of searching but I can't really find a source that doesn't consider those vectors that face in the opposite direction to not be parallel.

That might not make sense if you're defining parallel vectors as only being scalar multiples that face that same direction - but going by most sources it seems the definition of a parallel vector is that it would be scalar multiples that have the same or opposite direction (in other words just .

Dont make it so complicated. They are both parallel, anti-parallel just gives extra info that they are in opposite direction

BubbleWrapMan

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Re: Specialist 3/4 Question Thread!
« Reply #657 on: September 01, 2012, 08:26:36 pm »
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To me 'parallel' just means linearly dependent, i.e. one is a scalar multiple of the other, whether negative or positive.

can i please have help with this definite integral

0 to pi/4 tan^3(x) dx








Let and

Then and







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pi

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Re: Specialist 3/4 Question Thread!
« Reply #658 on: September 01, 2012, 08:32:46 pm »
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But you cant prove 2 vectors parallel just because their scalar multiples each other

That's the only way to prove that 2 vectors are parallel, that they are scalar multiples of eachother. If you're saying that you CAN'T prove 2 vectors are parallel to eachother by this method then how do you show that 2 vectors are parallel?


They are parallel if vector a=k*vector b. From there, you can say their scalar multiples each other

But you cant prove 2 vectors parallel just because their scalar multiples each other
For parallel vectors, is true. This is what it means for a vector to be a scalar multiple of another.

Your statement is a bit contradictory, you seem to be saying that they are parallel if , but you can't prove them parallel if they are That doesn't really make much sense to me.

Note that does imply that for when k is greater than 0. being true doesn't imply that they're parallel vectors. The example you gave in your previous post is an example of this. I think that's what you're getting at, and I think the confusion is whether we're talking about the vectors a and b, or if we're talking about the magnitudes of vectors a and b.

For parallel vectors, we are talking about the vectors.

Yeah, I was talking about multiplies of magnitudes

If generalkorn meant scalar multiplies of vectors, if k is positive => they are parallel. If k is negative => they are anti-parallel

I'm confused by this :/ Surely if k is negative the vectors are still parallel and the proof Paul is suggesting is valid.

Lasercookie

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Re: Specialist 3/4 Question Thread!
« Reply #659 on: September 01, 2012, 08:38:02 pm »
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Dont make it so complicated. They are both parallel, anti-parallel just gives extra info that they are in opposite direction
Oh my bad, I misinterpreted what you meant then. I thought you were implying that 'anti-parallel' wasn't parallel at all.