To determine the magnitude of the vector [tex]\(\vec{B} - \vec{A}\)[/tex], we start by calculating the components of this vector.
1. Components of the vectors:
- Vector [tex]\(\overrightarrow{ A }\)[/tex]: [tex]\((A_x = 2.2, A_y = -6.9)\)[/tex]
- Vector [tex]\(\overrightarrow{ B }\)[/tex]: [tex]\((B_x = -6.1, B_y = -2.2)\)[/tex]
2. Calculate the components of [tex]\(\vec{B} - \vec{A}\)[/tex]:
- The x-component of [tex]\(\vec{B} - \vec{A}\)[/tex] is:
[tex]\[
R_x = B_x - A_x = -6.1 - 2.2 = -8.3
\][/tex]
- The y-component of [tex]\(\vec{B} - \vec{A}\)[/tex] is:
[tex]\[
R_y = B_y - A_y = -2.2 - (-6.9) = -2.2 + 6.9 = 4.7
\][/tex]
3. Determine the magnitude of [tex]\(\vec{B} - \vec{A}\)[/tex]:
- The magnitude [tex]\( |\vec{B} - \vec{A}| \)[/tex] is calculated using the Pythagorean theorem:
[tex]\[
|\vec{B} - \vec{A}| = \sqrt{R_x^2 + R_y^2}
\][/tex]
Substituting the values of [tex]\(R_x\)[/tex] and [tex]\(R_y\)[/tex]:
[tex]\[
|\vec{B} - \vec{A}| = \sqrt{(-8.3)^2 + (4.7)^2}
\][/tex]
[tex]\[
|\vec{B} - \vec{A}| = \sqrt{68.89 + 22.09}
\][/tex]
[tex]\[
|\vec{B} - \vec{A}| = \sqrt{90.98}
\][/tex]
[tex]\[
|\vec{B} - \vec{A}| \approx 9.538
\][/tex]
Given the approximate magnitude of [tex]\(9.538\)[/tex], we can identify the closest value from the provided options:
A) 9.5
B) 6.1
C) 9.9
D) 91
Thus, the correct answer is:
A) 9.5
