https://file.aiquickdraw.com/mathbot/file/1727426567932ksp8bl6p.jpg

The image shows a vector, labeled as \( \vec{a} \), drawn on a coordinate grid. The prompt on the side in German translates to: "Draw vector 2 \( \vec{a} \) and label it."

Here’s a breakdown of the task:

1. You are asked to draw a new vector that is twice the length of \( \vec{a} \), which means scaling \( \vec{a} \) by a factor of 2. 
2. The vector \( \vec{a} \) appears to start at (0,0) and end at (3,2), giving it the coordinates \( \vec{a} = (3,2) \).
3. To find \( 2 \vec{a} \), multiply both components by 2:
   \[
   2 \vec{a} = 2 \times (3,2) = (6,4)
   \]
4. Draw this new vector starting from the origin (0,0) and ending at the point (6,4) on the grid.

Would you like more details or any further clarification?

Here are 5 questions related to this:

1. What is the direction of a vector relative to the x-axis?
2. How do you scale a vector by a scalar multiplier in general?
3. What is the difference between vector addition and scalar multiplication?
4. How would you find the magnitude of vector \( \vec{a} \)?
5. How can you graphically add two vectors?

**Tip:** When multiplying a vector by a scalar, only the length changes, not the direction, unless the scalar is negative!

Learn how to draw vector 2a on a coordinate grid by scaling the vector a by a factor of 2. Understand the basics of vector scaling and apply scalar multiplication to vector components. Suitable for students in Grades 9-11.

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