If `vecV=2veci+3vecj` and `vecY=veci-5vecj`, the resultant vector of `2vecU+3vecV` equals

Options

A. `3veci-2vecj`
B. `5veci+vecj`
C. `7veci-9vecj`
D. `8veci-vecj`

Explanation

To solve the problem, we need to find the resultant vector of \(2\vec{Y} + 3\vec{V}\) given:

\[ \vec{V} = 2\vec{i} + 3\vec{j} \]
\[ \vec{Y} = \vec{i} - 5\vec{j} \]

### Step-by-step Solution:

1. **Calculate \(2\vec{Y}\)**:
\[ 2\vec{Y} = 2(\vec{i} - 5\vec{j}) = 2\vec{i} - 10\vec{j} \]

2. **Calculate \(3\vec{V}\)**:
\[ 3\vec{V} = 3(2\vec{i} + 3\vec{j}) = 6\vec{i} + 9\vec{j} \]

3. **Add \(2\vec{Y}\) and \(3\vec{V}\)**:
\[ 2\vec{Y} + 3\vec{V} = (2\vec{i} - 10\vec{j}) + (6\vec{i} + 9\vec{j}) \]

4. **Combine like terms**:
- Combine the \(\vec{i}\) components:
\[ 2\vec{i} + 6\vec{i} = 8\vec{i} \]
- Combine the \(\vec{j}\) components:
\[ -10\vec{j} + 9\vec{j} = -1\vec{j} \]

5. **Write the resultant vector**:
\[ 2\vec{Y} + 3\vec{V} = 8\vec{i} - 1\vec{j} \]

Thus, the resultant vector is:
\[ \boxed{8\vec{i} - \vec{j}} \]