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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: BubbleWrapMan on December 04, 2010, 07:45:26 pm

Title: ajshfgsjkhgf vectors question
Post by: BubbleWrapMan on December 04, 2010, 07:45:26 pm
ABCD is a trapezium with AB parallel to DC. X and Y are midpoints of AD and BC respectively.

(It's laid out something like this)

  DC
 X  Y
A    B

a) Express (directed line segment) XY in terms of a and b where (directed line segment) AB = a and (directed line segment) DC = b
b) Show that XY is parallel to AB
Title: Re: ajshfgsjkhgf vectors question
Post by: BubbleWrapMan on December 04, 2010, 08:02:50 pm
I was thinking that, but the answer says (1/2)(a + b) which makes me think I'm missing something.
Title: Re: ajshfgsjkhgf vectors question
Post by: cipherpol on December 04, 2010, 08:04:05 pm
let and

or

Title: Re: ajshfgsjkhgf vectors question
Post by: 98.40_for_sure on December 04, 2010, 08:06:24 pm
Ahhah totally forgot you could define new vectors
Title: Re: ajshfgsjkhgf vectors question
Post by: BubbleWrapMan on December 04, 2010, 08:09:12 pm
Ah nice. Thanks everyone. ^^
Title: Re: ajshfgsjkhgf vectors question
Post by: 98.40_for_sure on December 04, 2010, 08:11:03 pm
Hey brightsky, why is a.b and a.a = 0?
Title: Re: ajshfgsjkhgf vectors question
Post by: BubbleWrapMan on December 04, 2010, 08:20:01 pm
I would have thought you'd just say something like

Since a and b are parallel, XY must be parallel to both, since a scalar multiplication of the sum of two parallel lines does not change the direction.
Title: Re: ajshfgsjkhgf vectors question
Post by: 98.40_for_sure on December 04, 2010, 08:21:53 pm
AB = a
since a = kb, XY = 1/2(a+ka) = 1/2(k+1)a

thus parallel?
Title: Re: ajshfgsjkhgf vectors question
Post by: BubbleWrapMan on December 04, 2010, 08:25:29 pm
Yeah. You're allowed to put it in words though aren't you? I've done it in the past.
Title: Re: ajshfgsjkhgf vectors question
Post by: 98.40_for_sure on December 04, 2010, 08:27:53 pm
Show that XY is parallel to AB.
Which means mathematical proof not 'explain'
Title: Re: ajshfgsjkhgf vectors question
Post by: BubbleWrapMan on December 04, 2010, 08:36:52 pm
Hmm. Good point. :P
Title: Re: ajshfgsjkhgf vectors question
Post by: brightsky on December 04, 2010, 08:41:30 pm
Quote from: 99.95_for_sure on December 04, 2010, 08:11:03 pm
Hey brightsky, why is a.b and a.a = 0?

Woops, I was thinking cross product. Listen to 99.95_for_sure. :p