VCE Specialist 3/4 Question Thread!

[rife168]

i + 2j - 3k and -9i +4j -k

^ find the Angle between the pair of vectors
(already found that the dot product is 2 from other part of the question)

And another question:

if (u-v) dot (u+v) = |v|^2, then:
A) u=v
B) u must be equal to the zero vector, O.
C) u perpendicular to v
D) u is multiple of v
E) None are true.

(nb: all us and vs etc have little squiggly things under them hehehe.
'dot' is that dot that just stands in space. If you get what i mean. The dot in dot product, the one that is off the floor, unlike this  . Why am i explaining all this, you prob figured anyway)
Thanks

I am going to represent the vectors like this because it's easier to type:


The dot product can be defined as follows:
where is the angle between the vectors.









     Is it a calculator question?

[Fishyiscool]

i + 2j - 3k and -9i +4j -k

^ find the Angle between the pair of vectors
(already found that the dot product is 2 from other part of the question)

And another question:

if (u-v) dot (u+v) = |v|^2, then:
A) u=v
B) u must be equal to the zero vector, O.
C) u perpendicular to v
D) u is multiple of v
E) None are true.

(nb: all us and vs etc have little squiggly things under them hehehe.
'dot' is that dot that just stands in space. If you get what i mean. The dot in dot product, the one that is off the floor, unlike this  . Why am i explaining all this, you prob figured anyway)
Thanks

I am going to represent the vectors like this because it's easier to type:


The dot product can be defined as follows:
where is the angle between the vectors.









     Is it a calculator question?

Thats what i got too! Yes it is a calc question, so i put that into my calc and got something like .. I dont know, it was really off frm what bob said.

[rife168]

i + 2j - 3k and -9i +4j -k

^ find the Angle between the pair of vectors
(already found that the dot product is 2 from other part of the question)

And another question:

if (u-v) dot (u+v) = |v|^2, then:
A) u=v
B) u must be equal to the zero vector, O.
C) u perpendicular to v
D) u is multiple of v
E) None are true.

(nb: all us and vs etc have little squiggly things under them hehehe.
'dot' is that dot that just stands in space. If you get what i mean. The dot in dot product, the one that is off the floor, unlike this  . Why am i explaining all this, you prob figured anyway)
Thanks

I am going to represent the vectors like this because it's easier to type:


The dot product can be defined as follows:
where is the angle between the vectors.









     Is it a calculator question?

Thats what i got too! Yes it is a calc question, so i put that into my calc and got something like .. I dont know, it was really off frm what bob said.

I got 1.51678 radians or 86.9 degrees

[soccerboi]

How do i draw a diagram for this:
For quadrilateral OABC , D is the point of trisection of OC nearer O and E is the point of trisection of AB nearer A.


Also this question: ABC is a right angled triangle with the right angle at B. If AC= 2i+4j and AB is parallel to i+j, find AB.

Could someone help me asap, cause i have a test tmr. Cheers

[rife168]

How do i draw a diagram for this:
For quadrilateral OABC , D is the point of trisection of OC nearer O and E is the point of trisection of AB nearer A.

See attachment
  and 


I have to go now so hopefully someone else can help with your other question

[Reckoner]

f(x)=(Ax^2 +Bx)/(x+C), where A,B and C are constants. The line x=-1 and y=x+4 are asymptotes to the curve. Find A,B and C.

Could someone please show me how to do this question? Thanks

[b^3]

Going to go over a little bit of theory in the explanation.

So we start off with
To find the asymptotes we have to split it up into its fractions, in other words we can long divide as below.



So that means that

Now we know there will be a vertical asymptote when the function results in something like which will be undefined. So that will be when , so

So we have a vertical asymptote at . Now we know that is an asymptote, so that means that here .

Now for the oblique asymptote, what happens as the fraction part gets smaller and smaller and approaches 0? The function will get closer and closer to , in other words approach it. So now we know that our other asymptote will be , corresponding to , so that means that and
Now solving for B


So that leaves us with the equation

You don't need all that wordy stuff in the solution, but its just there to explain it (hopefully).

Hope that helps, and hope there are not any mistakes

EDIT: Fixed some of the incomprehendable sentences.
EDIT2: Just thought I'd add the graph so that you can visualise the asymptotic behaviour of the oblique asymptote

[Reckoner]

Great answer! Really helped, thanks a lot!

[ashoni]

I need help with question 8b!

[DisaFear]

I need help with question 8b!

This isn't exactly spesh is it? D:

2P = 3a + 2(3b) + 2b + 3a = 6a + 8b (total perimeter)
A = 9ab + ab = 10ab

Answer must be in terms of a and P, so let's find b

8b + 6a = 2P
b= (2P - 6a)/8

Sub in b into the Area formula found before, A = 9ab + ab = 10ab

A = 10ab

A=(5aP - 15a^2)/2

Hope I didn't do anything wrong there. That'd be embarrassing

[pi]

I need help with question 8b!

This isn't exactly spesh is it? D:

2P = 3a + 2(3b) + 2b + 3a = 6a + 8b (total perimeter)
A = 9ab + ab = 10ab

Answer must be in terms of a and P, so let's find b

8b + 6a = 2P
b= (2P - 6a)/8

Sub in b into the Area formula found before, A = 9ab + ab = 10ab

A = (10aP - 3a)/4

Hope I didn't do anything wrong there. That'd be embarassing

2 issues:
1) You spelt that word wrong, two 'r's
2) A = 10a(P-3a)/4 = (10aP-30a^2)/4 = (5aP-15a^2)/2

[DisaFear]

Hey, spell check didn't pick it up

[pi]

Hey, spell check didn't pick it up

That's what VCE English was for!

And of course if wouldn't pick up the error in the fraction

Embarrassed?

[ashoni]

HAHAHA! nice spot VegemitePi!
But thanks for your help DisaFear!

[ashoni]

Another question!

 A man starts at 2 p.m. to walk to a place 26 km away. He walks at a constant speed until 4 p.m. when he increases his speed by 2 km/h. He reaches his destination at 5:30 p.m. At what speed did he walk for the first two hours?