Final answer:
The component form of vector v is determined by multiplying vector w by 2 and then adding it to vector u component-wise, resulting in the component form 4i + 3j.
Step-by-step explanation:
To find the component form of a vector v where v = u + 2w, and given u = 2i - j and w = i + 2j, we need to perform vector addition. We multiply vector w by 2 and then add it to vector u component-wise.
The resulting vector, in terms of its components, is calculated as follows:
- First, multiply w by 2: 2w = 2(i + 2j) = 2i + 4j.
- Then add this to u: v = u + 2w = (2i - j) + (2i + 4j).
- Combine the i and j components: v = (2+2)i + (-1+4)j = 4i + 3j.
Therefore, the component form of vector v is 4i + 3j.