https://r2.erweima.ai/mathbot/image/1725956279012xmgj4pi7.jpg

The image contains the following text in Russian:

**Translation:**
"If a vector \( \vec{a} \) is given by the coordinates \( \vec{a} = (a_1, a_2) \), then the length of the vector \( \vec{a} \) can be found using the formula ..."

The missing part of the sentence is likely the formula for the magnitude (or length) of a 2D vector, which is:

\[
|\vec{a}| = \sqrt{a_1^2 + a_2^2}
\]

This formula calculates the Euclidean length of the vector \( \vec{a} \) from its components \( a_1 \) and \( a_2 \).

Would you like further details on this formula or any related concepts?

Here are 5 related questions:
1. How can this formula be extended to 3D vectors?
2. What is the geometrical interpretation of the length of a vector?
3. How does this formula relate to the Pythagorean theorem?
4. Can the length of a vector be negative?
5. What are some applications of vector length in physics?

**Tip:** The length of a vector is often referred to as its magnitude or norm.

If a vector \( \vec{a} \) is given by the coordinates \( \vec{a} = (a_1, a_2) \), then the length of the vector \( \vec{a} \) can be found using the formula...

Learn how to calculate the length of a vector \( \vec{a} = (a_1, a_2) \) using the formula \( |\vec{a}| = \sqrt{a_1^2 + a_2^2} \), which is based on the Pythagorean theorem. This concept is essential in vector geometry and suitable for students in Grades 9-11.

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