Given:
The vectors are,
[tex]\begin{gathered} \vec{A}=6\text{ m west} \\ \vec{B}=11\text{ m south} \end{gathered}[/tex]
To find:
The subtraction,
[tex]\vec{A}-\vec{B}[/tex]
using graphical method
Explanation:
The representation of the vectors is shown below:
We can write,
[tex]\begin{gathered} \vec{A}-\vec{B} \\ =\vec{A}+(-\vec{B}) \end{gathered}[/tex]
This is represented in the image above.
The magnitude of the resultant is,
[tex]\begin{gathered} \lvert{\vec{A}-\vec{B}}\rvert=\sqrt{A^2+(-B)^2} \\ =\sqrt{6^2+(-11)^2} \\ =\sqrt{36+121} \\ =\sqrt{157} \\ =12.53\text{ m} \end{gathered}[/tex]
The angle with the east is,
[tex]\begin{gathered} \theta=tan^{-1}\frac{11}{6} \\ =61.39\degree \end{gathered}[/tex]
Hence, the resultant vector's magnitude and the direction are,
[tex]12.53\text{ m, 61.39}\degree[/tex]
