It looks like the image involves a mathematical diagram related to geometry. From the contents on the blackboard:

1. Diagram Analysis:

   • A triangle or geometric figure labeled with points $A$, $B$, $C$, and a point $O$ at the origin.
   • Vectors such as $\vec{a}$, $\vec{b}$, and $\vec{c}$ are involved.
   • There is a reference to coordinates and possibly to magnitudes of vectors.

2. Key Equations:

   • The equation $\left| \vec{a} + \vec{b} + \vec{c} \right|$ is highlighted.
   • There's a possible condition or geometric constraint, written in red: $\text{원에 내접하는 삼각형}$ which translates to "Triangle inscribed in a circle."
   • Another vector condition is indicated as $\vec{a} + \vec{b} + \vec{c} = 1$ or involving normalization.

3. Red Highlight:

   • $1 \cdot \vec{c} = b$: This might suggest a relationship or magnitude involving vectors.

4. Conclusion: This seems to be a lesson about vectors, their addition, and possibly properties of triangles inscribed in a circle. The geometric interpretation of vector magnitudes or constraints is central.

Would you like a detailed breakdown of:

• How vectors relate to inscribed triangles?
• How to interpret the magnitude $\left| \vec{a} + \vec{b} + \vec{c} \right|$?

Let me know how you'd like me to proceed! 😊

Related Questions:

1. What is the geometric significance of a triangle inscribed in a circle?
2. How do you add vectors geometrically and algebraically?
3. What is the condition for the sum of vectors to equal zero in a triangle?
4. How can vector magnitudes be normalized?
5. How do circles and triangles connect in coordinate geometry?

Tip:

The property of a triangle inscribed in a circle is linked to its circumcircle and the angles subtended by its sides.