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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,040

V # 1

Show that the vetcors a = (2,3,1), b = (5,-2,-4), and c = (10,-13,19) are mutually perpendicular.

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

a dot b = cosine of angle between them, cosine of 90 degrees is 0, so if a dot b is 0, they are perpendicular

a dot b = 2*5 + 3*-2 + 1*-4 = 10-6-4 = 0, a,b are perpendicular

a dot c = 2*10 + 3*-13 + 1*19 = 20 - 39 + 19 = 0, a,c are perpendicular

b dot c = 5*10 + -2*-13 + -4*19 = 50 + 26 - 76 = 0, b,c, are perpendicular

*Last edited by luca-deltodesco (2006-05-14 19:30:45)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,040

Very well done, luca-deltodesco!

Character is who you are when no one is looking.

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**angel_12****Member**- Registered: 2007-06-07
- Posts: 4

answer is already given...

waise that was a bit easy one!

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

i'd like to demand lots of vector proof problems, please!

can't find enough of them.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,889

hi ganesh

only one problem??? o.O

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