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2bornot2b

  • 2 years ago

I am trying to solve the following problem, and I have a solution which I don't understand, can you help me? "Show that in a triangle the perpendiculars drawn from the vertices are concurrent. "

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  1. 2bornot2b
    • 2 years ago
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    Here is the solution that I don't understand

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  2. Mani_Jha
    • 2 years ago
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    Exactly which part u dont understand? It is all about triangle law of vector addition and dot products

  3. 2bornot2b
    • 2 years ago
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    What has the solution shown so that its clear that the perpendiculars are concurrent.

  4. Mani_Jha
    • 2 years ago
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    Any two lines have to intersect(unless they are parallel). Now, if a third line passes through the intersection of these two lines, then the three are concurrent. In this solution, they have taken two perpendiculars. Through their intersection point a line has been drawn, and if that line happens to be the altitude through C, then all perpendiculars have to be concurrent. That's what we have to prove here. The dot product of two perpendicular lines is 0. So, we must prove that the dot product of AB and CF is zero. I hope it helped, if not please say

  5. 2bornot2b
    • 2 years ago
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    Just a sec, let me read it and understand

  6. 2bornot2b
    • 2 years ago
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    Have you seen they have used a constant like \(l\) while writing \[la(c-b)=0\] Whats the need of that \(l\)

  7. Mani_Jha
    • 2 years ago
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    Well, let me guess. Here OA=a. But actually we see that AD is perpendicular to BC and also intersects it. So, they took the length of AD instead of AO. So, AD/AO=l is assumed. so that al is the length of AD. But I dont think there is any compulsion of taking l and m here.

  8. 2bornot2b
    • 2 years ago
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    Do you have any better solution for it?

  9. Mani_Jha
    • 2 years ago
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    Of course there is a geometrical solution to this. Well, let me work on it. I will post it as soon as i complete it

  10. 2bornot2b
    • 2 years ago
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    No thank you, I need to make it through vector

  11. 2bornot2b
    • 2 years ago
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    Thats mandatory for me

  12. 2bornot2b
    • 2 years ago
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    OK, thank you!

  13. 2bornot2b
    • 2 years ago
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    OK so mani jha provided with the explanation that " The dot product of two perpendicular lines is 0. So, we must prove that the dot product of AB and CF is zero. I hope it helped, if not please say", but it didn't quite satisfy me. Can you think of any better explanation. Does this solution have anything to do with vector equation?

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