Naming a triangle for a vectors question

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SUMMARY

The discussion focuses on calculating the angle ACB in triangle ABC with vertices A (−1, 3,−3), B (2, 4, 6), and C (3, 0,−5) using the scalar product method. The user attempted to derive the angle using vector equations and the scalar product formula, resulting in an angle of approximately 104.197°. However, the user expressed concern about the validity of this result, questioning whether their calculations were correct. The vectors were defined as a = -i + 3j - 3k, b = 2i + 4j + 6k, and c = 3i - 5k.

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Homework Statement



Triangle ABC has A (−1, 3,−3), B (2, 4, 6) and C (3, 0,−5). Use the scalar
product to find the angle ACB.
No pictures are given



The Attempt at a Solution



I have attempted the question by naming the triangle ABC with each angle opposite the line with the same name.
The I have changed A B and C into vector equations and used the scalar product between A and B to get the angle C.
This does not seem to be working.
I end up with

-8=√56√19cos(C)

c=104.197°


This seems like a bit of a crazy answer am I doing it wrong?
 
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mazz1801 said:

Homework Statement



Triangle ABC has A (−1, 3,−3), B (2, 4, 6) and C (3, 0,−5). Use the scalar
product to find the angle ACB.

No pictures are given

The Attempt at a Solution



I have attempted the question by naming the triangle ABC with each angle opposite the line with the same name.
The I have changed A B and C into vector equations and used the scalar product between A and B to get the angle C.
This does not seem to be working.
I end up with

-8=√56√19cos(C)

c=104.197°This seems like a bit of a crazy answer am I doing it wrong?
I don't see how anyone can tell you whether what you did was wrong when you haven't said what you did! What did you get for the vectors? What did you get for the lengths of those vectors?
 
sorry I thought I had given enough info.

a= -i+3j-3k
b= 2i+4j+6k
c= 3i -5k

to find andle ACB by scalar product
a.b=|a||b|cos(c)

a.b= -8
|a|= √56
|b|= √19

so
-8=√56√19cos(c)

cos(c)=(-8) / (√56√19)

so c=cos-1((-8) / (√56√19))
c=104.197°
 

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