Certainly! Let's solve this problem step by step.
Step 1: Identify the components of the vectors.
We have three vectors [tex]\( S \)[/tex], [tex]\( T \)[/tex], and [tex]\( U \)[/tex] with the following components:
[tex]\[
\begin{array}{c|c|c}
& \text{x-comp} & \text{y-comp} \\
\hline
S & 3.50 & -4.50 \\
T & 2.00 & 0.00 \\
U & -5.50 & 2.50 \\
\end{array}
\][/tex]
Step 2: Calculate the x-component of the resultant vector [tex]\( R \)[/tex].
The x-component of the resultant vector [tex]\( R \)[/tex] is the sum of the x-components of [tex]\( S \)[/tex], [tex]\( T \)[/tex], and [tex]\( U \)[/tex]:
[tex]\[
\text{x-comp of } R = S_x + T_x + U_x = 3.50 + 2.00 + (-5.50) = 0.00
\][/tex]
Step 3: Calculate the y-component of the resultant vector [tex]\( R \)[/tex].
The y-component of the resultant vector [tex]\( R \)[/tex] is the sum of the y-components of [tex]\( S \)[/tex], [tex]\( T \)[/tex], and [tex]\( U \)[/tex]:
[tex]\[
\text{y-comp of } R = S_y + T_y + U_y = -4.50 + 0.00 + 2.50 = -2.00
\][/tex]
Step 4: Calculate the magnitude of the resultant vector [tex]\( R \)[/tex].
The magnitude of the resultant vector [tex]\( R \)[/tex] can be found using the Pythagorean theorem:
[tex]\[
|R| = \sqrt{(\text{x-comp of } R)^2 + (\text{y-comp of } R)^2}
\][/tex]
Substituting in the components calculated earlier:
[tex]\[
|R| = \sqrt{(0.00)^2 + (-2.00)^2} = \sqrt{0.00 + 4.00} = \sqrt{4.00} = 2.00
\][/tex]
Step 5: Determine the correct answer.
The magnitude of the resultant vector is [tex]\( 2.0 \)[/tex]. Therefore, the correct answer is:
[tex]\[
\text{B) 2.0}
\][/tex]
