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March 29, 2024, 09:00:42 am

Author Topic: Vector Question  (Read 4069 times)  Share 

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APK911

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Vector Question
« on: October 02, 2017, 04:08:59 pm »
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The line r=(2i+3j-k) +t(-i+3j+k) passes through A (where t=1) and B (where t=5). Find the position vector of point C where AC:BA=-1:4

Any help would be appreciated, thank you in advance!

Syndicate

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Re: Vector Question
« Reply #1 on: October 02, 2017, 05:23:29 pm »
+6
The line r=(2i+3j-k) +t(-i+3j+k) passes through A (where t=1) and B (where t=5). Find the position vector of point C where AC:BA=-1:4

Any help would be appreciated, thank you in advance!

AC:BA = -1:4 implies CA:BA = 1:4.

OA = i+6j
OB= -3i+18j+4k

BA = -OB + OA
= 4i-12j-4k

multiply BA by 4
=> 16i - 48j -16k

CA = -OC + OA
Therefore
-OC + i+6j = 16i-48j-16k
Therefore OC = -15i + 54j +16k (when t = 17)

Never really done this sort of question before, so if I am wrong feel free to correct me.
« Last Edit: October 02, 2017, 05:26:06 pm by Syndicate »
2017: Chemistry | Physics | English | Specialist Mathematics | Mathematics Methods
2018-2020 : Bachelor of Biomedicine at University of Melbourne

Physics Guide 2017

APK911

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Re: Vector Question
« Reply #2 on: October 02, 2017, 05:48:42 pm »
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Thank you very much for the reply! That's exactly what I did, but the answer seems to be wrong. The answer is 9j+k  :-\
« Last Edit: October 02, 2017, 06:17:48 pm by APK911 »

VanillaRice

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Re: Vector Question
« Reply #3 on: October 02, 2017, 06:01:38 pm »
+5
Th ank you very much for the reply! That's exactly what I did, but the answer seems to be wrong. The answer is 9j+k  :-\
Syndicate's working out is almost correct, except that you should divide BA by 4 (rather than multiplying). This is another case of ratios being confusing (it always used to confuse me as well  :-[). CA:BA = 1:4 implies BA is bigger, so CA = (1/4)BA

Hope this helps :)
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APK911

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Re: Vector Question
« Reply #4 on: October 02, 2017, 06:15:57 pm »
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Thank you very much!!!! Yea these negative ratios are especially confusing...

Syndicate

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Re: Vector Question
« Reply #5 on: October 02, 2017, 06:51:47 pm »
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Syndicate's working out is almost correct, except that you should divide BA by 4 (rather than multiplying). This is another case of ratios being confusing (it always used to confuse me as well  :-[). CA:BA = 1:4 implies BA is bigger, so CA = (1/4)BA

Hope this helps :)

Thanks. I knew I did something wrong :P
2017: Chemistry | Physics | English | Specialist Mathematics | Mathematics Methods
2018-2020 : Bachelor of Biomedicine at University of Melbourne

Physics Guide 2017