Naming a triangle for a vectors question

In summary, the angle ACB in triangle ABC with vertices A(-1,3,-3), B(2,4,6), and C(3,0,-5) can be found using the scalar product. By finding the dot product of vectors A and B and dividing it by the product of the magnitudes of A and B, the cosine of angle ACB can be determined. Using the inverse cosine function, the angle is calculated to be 104.197°.
  • #1
mazz1801
23
0

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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  • #2
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?
 
  • #3
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°
 

1. How do I name a triangle for a vectors question?

In order to name a triangle for a vectors question, you will need to use the three vertices of the triangle. You can label the vertices as A, B, and C and then use the order in which they appear to name the triangle. For example, if vertex A is the first point, vertex B is the second point, and vertex C is the third point, you can name the triangle as triangle ABC.

2. What is the purpose of naming a triangle in a vectors question?

Naming a triangle in a vectors question helps to identify and distinguish the triangle from others in the problem. It also allows you to easily refer to specific angles or sides of the triangle when solving the question.

3. Can I use any letters to name a triangle for a vectors question?

Yes, you can use any letters to name a triangle for a vectors question. However, it is important to use a consistent order when naming the vertices to avoid confusion.

4. Do I need to name all three sides of the triangle in a vectors question?

No, you do not need to name all three sides of the triangle in a vectors question. Usually, only two sides are needed to represent a vector. However, if all three sides are given in the question, it is helpful to name them for reference.

5. How do I determine the direction of a vector in a triangle?

The direction of a vector in a triangle can be determined by the order in which the vertices are named. For example, if vector AB is pointing from point A to point B, then vector BA would be pointing in the opposite direction, from point B to point A.

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