Explanation
In the question, we are given the vectors
[tex]\begin{gathered} a=(-5,10) \\ g=(4,\text{ 12)} \end{gathered}[/tex]
First, we will find the vector 9a-g.
[tex]\begin{gathered} 9a-g=9\times-5i+9\times10j-4i-12j \\ =-45i+90j-4i-12j \\ =-49i+78j \end{gathered}[/tex]
We can find the resultant and angle of the vector with the formulas below.
[tex]\begin{gathered} R=\sqrt[]{x^2+y^2} \\ \theta=\tan ^{-1}\frac{y}{x} \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} R=\sqrt[]{(-49)^2+78^2}=\sqrt[]{8485}=92.114 \\ \theta=tan^{-1}=\frac{78}{-49}=-57.86^0\Rightarrow122.14^0 \end{gathered}[/tex]
Answer: Option A
