Question

I need to find the magnitude and direction angle of the resultant vector. I am having trouble with this.

Answer 1

Step-by-step explanation

In the question, we are given the vectors

`\begin{gathered} a=(-5,10) \\ g=(4,\text{ 12)} \end{gathered}`

First, we will find the vector 9a-g.

`\begin{gathered} 9a-g=9*-5i+9*10j-4i-12j \\ =-45i+90j-4i-12j \\ =-49i+78j \end{gathered}`

We can find the resultant and angle of the vector with the formulas below.

`\begin{gathered} R=\sqrt[]{x^2+y^2} \\ \theta=\tan ^(-1)(y)/(x) \end{gathered}`

Therefore,

`\begin{gathered} R=\sqrt[]{(-49)^2+78^2}=\sqrt[]{8485}=92.114 \\ \theta=tan^(-1)=(78)/(-49)=-57.86^0\Rightarrow122.14^0 \end{gathered}`

Answer: Option A