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!