VCE Specialist 3/4 Question Thread!

[fadzsta1]

Ah yes, forgot to divide the domain by 2. Excellent, thanks brightsky! Much appreciated

[alchemy]

I'm looking for a simpler way of doing the attached question. My answer is correct but I had to find the individual values of AP and AB from the values of t and n. This is a tech-free question and my method would have taken longer than necessary by hand as it involved manipulating many fractions.
The attached answers are attached and indicate a seemingly shorter method.

[scribble]

have no clue what theyre doing in the solutions, but this is how i'd do it. it doesn't seem like *too* much work.
sorry if you can't follow my super sloppy, halfassed working. more or less, i found AB, then found AP by using the given coordinates and solving simultaneously. once you have AP in terms of a constant and AB, its easy to say what the ratio is. 

[Stick]

Not related to the purpose of this thread, but you have a very interesting fingernail.

[alchemy]

have no clue what theyre doing in the solutions, but this is how i'd do it. it doesn't seem like *too* much work.
sorry if you can't follow my super sloppy, halfassed working. more or less, i found AB, then found AP by using the given coordinates and solving simultaneously. once you have AP in terms of a constant and AB, its easy to say what the ratio is.

Yeah, that's pretty much what I did. It looked as if it could've been done much more simply from the solutions though. Thanks for that well presented explanation (:

Not related to the purpose of this thread, but you have a very interesting fingernail.

LOL!

[Thorium]

Hi, how do I prove that the diagonals of a parallelogram bisect each other? (using vectors)

[alchemy]

Hi, how do I prove that the diagonals of a parallelogram bisect each other? (using vectors)

Hey Alisina,
Please refer to the attached diagram. Sorry, it was rushed through and doesn't really look exactly like a parallelogram.
Let's say we have a parallelogram ABCD. We can use the property of linear independence to prove that the diagonals bisect each other.

Let AB = DC = a and DA = CB = b, where a and b are vectors.
AC = AB + BC = a - b and DB = DC + CB = a + b
Let AO = xAC  = x(a-b) and DO = yDB = y(a+b)
Now consider triangle AOD: DA = DO + OA = DO - AO
But DA = b, DO = y(a+b) and AO = x(a-b)
Hence, b = y(a+b) - x(a-b)
b = ya + yb -xa +xb = (y-x)a + (y+x)b
(y-x)a + (y+x-1)b = 0
Since a and b are linearly independent:
y-x=0
y+x-1=0
Solve both these equations simultaneously to get x=1/2 and y=1/2
This tells us that O is the midpoint of diagonals AC and DB.
Hope that helps (:

[Thorium]

Let AB = DC = a and DA = CB = b, where a and b are vectors.
AC = AB + BC = a - b and DB = DC + CB = a + b
Let AO = xAC  = x(a-b) and DO = yDB = y(a+b)
Now consider triangle AOD: DA = DO + OA = DO - AO
But DA = b, DO = y(a+b) and AO = x(a-b)
Hence, b = y(a+b) - x(a-b)
b = ya + yb -xa +xb = (y-x)a + (y+x)b
(y-x)a + (y+x-1)b = 0
Since a and b are linearly independent:
y-x=0
y+x-1=0
Solve both these equations simultaneously to get x=1/2 and y=1/2
This tells us that O is the midpoint of diagonals AC and DB.
Hope that helps (:

Thanks Alchemy

[scribble]

Not related to the purpose of this thread, but you have a very interesting fingernail.

lmao leave my obnoxious princess nails alone! it's to remind me to eat more fruit. :'D
(i am actually an overgrown three year old)

[Stick]

lmao leave my obnoxious princess nails alone! it's to remind me to eat more fruit. :'D
(i am actually an overgrown three year old)

It was a compliment!

[Nato]

do you always need to factor vectors:

For example for one question i got an answer (which i didn't completely factor) of:


and in the answers, they had written:
.

so, i was just wondering if my answer is acceptable, or would marks be deducted.

[lzxnl]

I highly doubt you'd have to "simplify" your answer further. I don't think I always did.

[bucklr]

do you always need to factor vectors:

For example for one question i got an answer (which i didn't completely factor) of:


and in the answers, they had written:
.

so, i was just wondering if my answer is acceptable, or would marks be deducted.

Apparently they used to penalise but not any more. Examiners will credit equivalent answers.

[Thorium]

Hi, a question asks me to prove the cosine rule using vectors. What I did was that I used dot product, but I couldnt get the exact formula. Instead I got (a^2+b^2-2ab)cosx. Can anyone please help me find the correct ans?

[b^3]

EDIT: Added a diagram.