Answer:
122°
Step-by-step explanation:
To find the angle between two vectors (forces are vectors), we need to use
[tex]cos\theta=\frac{F_{1} * F_{2} }{|F_{1}| \times |F_{2}|}[/tex]
Where
[tex]F_{1}=-1i+4j[/tex]
[tex]F_{2}=3i-1j[/tex]
First, we need to find the length of each vector
[tex]|F_{1}|=\sqrt{(4)^{2}+(-1)^{2} } =\sqrt{16+1} =\sqrt{17} \\|F_{2}|=\sqrt{(-1)^{2}+(3)^{2} } =\sqrt{1+9} =\sqrt{10}[/tex]
Then, we calculate the fot product of the vectors
[tex]F_{1} * F_{2}=(-1)(3)+(4)(-1)=-3-4=-7[/tex]
Now, we replace all in the formula
[tex]cos\theta=\frac{-7}{\sqrt{17} \times \sqrt{10} } =-\frac{7}{\sqrt{170} } \\\theta = cos^{-1}(-\frac{7}{\sqrt{170} }) \approx 122.6 \°[/tex]
Therefore, the right answer is the second choice 122°.
