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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Glockmeister on June 23, 2008, 06:03:14 pm

Title: I swear I hate vectors
Post by: Glockmeister on June 23, 2008, 06:03:14 pm: From my assignment:

   Two objects, A and B, are moving so that their positions (in metres) from the origin O, at time t seconds are represented by the vectors,
   a(t) = 3ti + (1-t)j and b(t) = (3 + sin $\frac{\pi t}{6}$ )i + (1 - cos $\frac{\pi t}{6}$ )j, t , respectively.
   (a) Find the exact position vector of each object at t = 2.
   (b) Find in exact form at t = 2.
   (c ) Hence find the distance between the two objects at t = 2, correct to 2 decimal places.
   (d) At t = 2, an observer at O is looking at object A. Through what angle (correct to the nearest minute) must the observer turn to be looking at B?

I can do a,b and c, but I can't seem to get d
Title: Re: I swear I hate vectors
Post by: Mao on June 23, 2008, 06:39:18 pm: at t=2

$\vec{a}(2)=6i-j$

$\vec{b}(2)=\left( 3+\frac{\sqrt{3}}{2}\right) i + \frac{1}{2}j$

$|\vec{a}(2)|=\sqrt{37}$

$|\vec{b}(2)|=\sqrt{\frac{1+(6+\sqrt{3})^2}{4}}$

$\theta = \cos^{-1}\frac{\vec{a}(2)\cdot \vec{b}(2)}{|\vec{a}(2)|\cdot |\vec{b}(2)|}$

$\implies \theta = \cos^{-1}\frac{6\left( 3+\frac{\sqrt{3}}{2}\right)-\frac{1}{2}}{\sqrt{37\cdot \left( \frac{1+(6+\sqrt{3})^2}{4}\right) }}=\mbox{blah~}$
Title: Re: I swear I hate vectors
Post by: Glockmeister on June 23, 2008, 06:46:29 pm: That's the answer I got, but when I put it in the calc, it gives a domain error.
Title: Re: I swear I hate vectors
Post by: Mao on June 23, 2008, 08:31:38 pm: did you type it correctly? :P

$\theta \approx \cos^{-1} 0.95716 \approx 16^o 50'$
Title: Re: I swear I hate vectors
Post by: Glockmeister on June 23, 2008, 11:14:55 pm: Heh, I get 19.something but I'm, going to trust your calculation more (I honestly gotta by that CAS calculator).
Title: Re: I swear I hate vectors
Post by: ell on June 23, 2008, 11:52:10 pm: Quote from: Glockmeister on June 23, 2008, 11:14:55 pm
Heh, I get 19.something but I'm, going to trust your calculation more (I honestly gotta by that CAS calculator).

You should get one, they're really worth the money.
Title: Re: I swear I hate vectors
Post by: Glockmeister on June 24, 2008, 12:41:57 am: sigh shouldve done methods CAS instead lol
Title: Re: I swear I hate vectors
Post by: Mao on June 24, 2008, 02:56:14 pm: Quote from: Glockmeister on June 23, 2008, 11:14:55 pm
Heh, I get 19.something but I'm, going to trust your calculation more (I honestly gotta by that CAS calculator).

that was with a scientific calculator :P
Title: Re: I swear I hate vectors
Post by: dcc on June 24, 2008, 03:33:39 pm: Quote from: Glockmeister on June 24, 2008, 12:41:57 am
sigh shouldve done methods CAS instead lol

Glockmeister, you and me, with our rustic non-CAS calculator for Specialist will absolutely dominate it up :) (Trust me, Spec examiners are not allowed to impart any large advantage on students who can afford a CAS calculator) :P
Title: Re: I swear I hate vectors
Post by: Glockmeister on June 24, 2008, 05:06:30 pm: Lol, your confident.

*dances with dcc*
Title: Re: I swear I hate vectors
Post by: Mao on June 24, 2008, 05:35:32 pm: Quote from: dcc on June 24, 2008, 03:33:39 pm
Quote from: Glockmeister on June 24, 2008, 12:41:57 am
sigh shouldve done methods CAS instead lol

Glockmeister, you and me, with our rustic non-CAS calculator for Specialist will absolutely dominate it up :) (Trust me, Spec examiners are not allowed to impart any large advantage on students who can afford a CAS calculator) :P

never~ :P

[i'm sure you are right :) ]
Title: Re: I swear I hate vectors
Post by: /0 on June 25, 2008, 07:29:26 am: In the Methods CAS exam you're not allowed to bring in a non-CAS calculator! That means scientific calculators are not allowed! Lololololol that's a pretty stupid rule
Title: Re: I swear I hate vectors
Post by: cara.mel on June 25, 2008, 11:06:40 am: Quote from: DivideBy0 on June 25, 2008, 07:29:26 am
In the Methods CAS exam you're not allowed to bring in a non-CAS calculator! That means scientific calculators are not allowed! Lololololol that's a pretty stupid rule

Scientific calculators != non-CAS graphics calculators. You can have a scientific one and a graphics one, but not two graphics ones

http://www.vcaa.vic.edu.au/vce/studies/mathematics/approvedcalculators.html
"For specified mathematics examinations, either one approved graphics calculator or one approved CAS may be used, as applicable to that study. A scientific calculator may also be used if desired. Students are not allowed to take into any examination a CAS and a graphics calculator."
Title: Re: I swear I hate vectors
Post by: /0 on June 26, 2008, 06:14:37 am: Well that's what i read on a handout
Title: Re: I swear I hate vectors
Post by: Mao on June 26, 2008, 12:28:14 pm: Quote from: DivideBy0 on June 26, 2008, 06:14:37 am
Well that's what i read on a handout

scientific calcs are definitely allowed.
i took both in and no one killed me :)
Title: Re: I swear I hate vectors
Post by: cara.mel on June 26, 2008, 12:54:34 pm: Quote from: Mao on June 26, 2008, 12:28:14 pm
Quote from: DivideBy0 on June 26, 2008, 06:14:37 am
Well that's what i read on a handout

scientific calcs are definitely allowed.
i took both in and no one killed me :)

The supervisors are trained to kill now? :(