Ibv9 The triangle ABC is defined by the following vectors

In summary, the triangle ABC is a geometric representation of the three vectors that define the vector IBv9. The vectors AB, BC, and CA are related to each other through the laws of cosines and sines. The triangle ABC can provide information about the magnitude and direction of vector IBv9, as well as be used in calculations involving the dot and cross product. Vector IBv9 is represented by the diagonal of the triangle ABC, and this representation has many applications in scientific fields such as physics, engineering, and mathematics.
  • #1
karush
Gold Member
MHB
3,269
5
View attachment 1227
this is best I can figure for the triangle (shaded)
but \(\displaystyle \vec{OC}\) looks like it has decimals in it.
View attachment 1226
 
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  • #2
Good picture, I think. Can you write down the $x$-component of $OC$ immediately? If so, can you think of a way, maybe, to write down an equation governing where the $y$-component must be?
 
  • #3
At $x=2, y=\frac{13}{4}$
 
  • #4
karush said:
At $x=2, y=\frac{13}{4}$

You've got it, except for notation. $OC=?$
 
  • #5
Ackbach said:
You've got it, except for notation. $OC=?$

\(\displaystyle \vec{OC} = \pmatrix{2 \\ 3.25}\):D
 
  • #6
karush said:
\(\displaystyle \vec{OC} = \pmatrix{2 \\ 3.25}\):D

(Clapping)
 

FAQ: Ibv9 The triangle ABC is defined by the following vectors

What is the significance of the triangle ABC in the context of vector IBv9?

The triangle ABC is a geometric representation of the three vectors that define the vector IBv9. These vectors, AB, BC, and CA, together form the sides of the triangle and are used to calculate various properties of vector IBv9.

How are the vectors AB, BC, and CA related to each other in triangle ABC?

The vectors AB, BC, and CA are related to each other through the law of cosines and the law of sines. These laws describe how the lengths and angles of the sides of a triangle are related to each other.

What information can be derived from the triangle ABC in relation to vector IBv9?

The triangle ABC can provide information about the magnitude and direction of vector IBv9. It can also be used to calculate the dot product and cross product of vector IBv9 with other vectors.

How is vector IBv9 represented in the triangle ABC?

Vector IBv9 is represented by the diagonal of the triangle ABC, which connects the points A and C. The direction of vector IBv9 can be determined by the orientation of this diagonal within the triangle.

What are some common applications of vector IBv9 and the triangle ABC in scientific fields?

Vector IBv9 and the triangle ABC have many applications in fields such as physics, engineering, and mathematics. They are commonly used in calculations involving forces, velocities, and rotations in three-dimensional space.

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