Given:-
[tex]v=-8i-5j,w=3i-j[/tex]
To find the angle between v and w.
So now we use the formula,
[tex]cos\theta=\frac{v.w}{\left|w\right|\left|v\right|}[/tex]
So now we find the dot product of the given vectors. so we get,
[tex]\begin{gathered} v.w=-8(3)+(5) \\ v.w=-24+5 \\ v.w=-19 \end{gathered}[/tex]
Also now we find the modulus values,
[tex]\left|v\right|=\sqrt{8^2+5^2}=\sqrt{64+25}=\sqrt{89}[/tex]
Also,
[tex]\left|w\right|=\sqrt{9+1}=\sqrt{10}[/tex]
Substituting we get,
[tex]\theta=cos^{-1}(-\frac{19}{\sqrt{81}\sqrt{10}})[/tex]
