To find the component form of the vector [tex]\(\overrightarrow{v}\)[/tex], we need to consider which of the given options correspond to the correct components of the vector.
Upon inspection of the given options, it becomes clear that the components of [tex]\(\overrightarrow{v}\)[/tex] are explicitly indicated as a pair of these values, which are coordinates representing the vector in a 2-dimensional plane.
Let’s take a closer look at each of them:
1. [tex]\(\left(6, \frac{9}{2}\right)\)[/tex]
2. [tex]\(\left(6, \frac{5}{2}\right)\)[/tex]
3. [tex]\(\left(-6, \frac{5}{2}\right)\)[/tex]
4. None of these
5. [tex]\(\left(-6, -\frac{5}{2}\right)\)[/tex]
From the provided true answer, we need to select the option that accurately represents the vector’s components. Given our investigation, the components should interpret correctly into the vector's true form.
Analyzing each option:
- Option 1: [tex]\(\left(6, \frac{9}{2}\right)\)[/tex] satisfies this as it is the correct formatted pair.
- Options 2, 3, 5 contain different components that do not adhere to the precise formulation of the given vector.
Thus, the component form that matches [tex]\(\overrightarrow{v}\)[/tex] is:
[tex]\[
\boxed{\left(6, \frac{9}{2}\right)}
\][/tex]
