Login

Search the forums now!

Welcome, Guest. Please login or register.

June 08, 2026, 05:19:11 am
Pages: [1] 2   Go Down

Author Topic: Bawse's SM Question Thread  (Read 2821 times)  Share 

0 Members and 1 Guest are viewing this topic.

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Bawse's SM Question Thread
« on: March 14, 2011, 05:08:42 pm »
0


Thanks

EDIT: Making this my SM question thread.
« Last Edit: March 14, 2011, 05:54:24 pm by bawse »
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

luken93

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3060
  • Respect: +114
Re: How to do this question?
« Reply #1 on: March 14, 2011, 05:36:58 pm »
0
If the two diagonals intersect at right angles, then

Let Diagonal 1 = DB; Diagonal B = AC



DB = b - d = 4i - j -(2i - 6j)   =   4i - j -2i + 6j   =   2i + 5j

AC = c - a = 5i - 3j -(-5i + j)   =   5i - 3j + 5i - j   =   10i - 4j

Now dot product:

a1 x b1 + a2 x b2
= (2 x 10) + (5 x -4)
= 20 - 20
= 0

As required


Logged
2010: Business Management [47]
2011: English [44]   |   Chemistry [45]  |   Methods [44]   |   Specialist [42]   |   MUEP Chemistry [5.0]   |   ATAR: 99.60
UMAT: 69 | 56 | 82 | = [69 / 98th Percentile]
2012: MBBS I @ Monash

brightsky

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3136
  • Respect: +200
Re: How to do this question?
« Reply #2 on: March 14, 2011, 05:39:21 pm »
0
Still learning how to do vectors so forgive me if there are any errors:
Let's denote A = -5i + j, B = 4i - j, C = 5i - 3j, D = 2i - 6j
Diagonal AC = AO + OC = 5i - j + 5i - 3j = 10i - 4j
Diagonal BD = BO + OD = -4i + j + 2i - 6j = -2i - 5j
By dot product formula:
(10i - 4j)(-2i - 5j) = sqrt(100 + 16)sqrt(4 + 25) cos(theta)
-20 + 20 = sqrt(116)sqrt(29) cos(theta)
cos(theta) = 0
theta = 90

EDIT: Beaten.
Logged
2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Re: How to do this question?
« Reply #3 on: March 14, 2011, 05:53:33 pm »
0
Thank you very much guys!
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Re: Bawse's SM Question Thread
« Reply #4 on: March 14, 2011, 09:15:22 pm »
0


Another one I can't get my head around :(
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Re: Bawse's SM Question Thread
« Reply #5 on: March 15, 2011, 09:20:15 pm »
0
Bump!
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Re: Bawse's SM Question Thread
« Reply #6 on: March 16, 2011, 08:45:23 pm »
0
I'm sure there's a more elegant way. My hackworks gives this:

We can express OA = OB + BA = OB - AB, OC = OD + DC = OD + AB

Thus OA.OC = (OB-AB).(OD+AB) = OB.OD + OB.AB - OD.AB - AB.AB = OB.OD + (OB-OD-AB).AB

We specifically look at OB - OD - AB = OB + DO + BA = DO + OB + BA = DA
Thus (OB-OD-AB).AB = DA.AB = 0

Therefore OA.OC = OB.OD

QED.

Logged
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

luken93

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3060
  • Respect: +114
Re: Bawse's SM Question Thread
« Reply #7 on: March 16, 2011, 08:48:38 pm »
0
Quote from: Mao on March 16, 2011, 08:45:23 pm
I'm sure there's a more elegant way. My hackworks gives this:
That's why I didn't answer, there is really no nice way about it?

Is there really any nice way to prove that O isn't on the same plane?
Logged
2010: Business Management [47]
2011: English [44]   |   Chemistry [45]  |   Methods [44]   |   Specialist [42]   |   MUEP Chemistry [5.0]   |   ATAR: 99.60
UMAT: 69 | 56 | 82 | = [69 / 98th Percentile]
2012: MBBS I @ Monash

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Re: Bawse's SM Question Thread
« Reply #8 on: March 17, 2011, 06:50:52 pm »
0
I actually attempted it a similar way but I felt like you Mao in that thinking there was a more elegant way.

Thank you!
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

enpassant

  • Guest
Re: Bawse's SM Question Thread
« Reply #9 on: March 18, 2011, 08:53:46 am »
0
(OB+OD).(OB+OD)=(OA+OC).(OA+OC) .... (1) Let you fig out why.
(OB-OD).(OB-OD)=(OA-OC).(OA-OC) .... (2) Let you fig out why.

(1) - (2) GIVES THE RESULT.
Logged

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Re: Bawse's SM Question Thread
« Reply #10 on: March 18, 2011, 11:27:14 am »
0
Quote from: enpassant on March 18, 2011, 08:53:46 am
(OB+OD).(OB+OD)=(OA+OC).(OA+OC) .... (1) Let you fig out why.
(OB-OD).(OB-OD)=(OA-OC).(OA-OC) .... (2) Let you fig out why.

(1) - (2) GIVES THE RESULT.

Very nice.

For (1), OB+OD = OA+OC = 2OX, where X is the center of the rectangle. OB-OD and OA-OC represent the diagonals, the rest is trivial.
Logged
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Re: Bawse's SM Question Thread
« Reply #11 on: March 18, 2011, 04:18:53 pm »
0
Thank you :)
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

bawse

  • Victorian
  • Forum Regular
  • **
  • Posts: 77
  • I can't believe I ate the whole thing
  • Respect: +4
Re: Bawse's SM Question Thread
« Reply #12 on: March 27, 2011, 01:05:02 am »
0
Jeff is picturing his position as if he was on an Argand diagram. He's standing at point G on level ground 8 units from the origin on a 45 degree angle.

Let c represent point G.

If c represents a solution to a cubic equation, what are the other solutions?
Logged
Biology, Chemistry, English, Methods, Specialist

Aim: 80+

enpassant

  • Guest
Re: Bawse's SM Question Thread
« Reply #13 on: March 27, 2011, 07:12:56 am »
0
8, 165 deg; 8, -75 deg
Logged

VCE247

  • Guest
Re: Bawse's SM Question Thread
« Reply #14 on: March 27, 2011, 09:58:57 am »
0
how did you get that?
Logged
Pages: [1] 2   Go Up