Answer:
The angle between u and v is 142°
C is correct
Step-by-step explanation:
Given: [tex]\vec{u}=3i+\sqrt{3}j[/tex]
[tex]\vec{v}=-2i-5j[/tex]
We need to find the angle between u and v vector.
Using dot product.
[tex]\vec{u}\cdot \vec{v}=|u||v|\cos\theta[/tex]
where,
[tex]\theta\text{ is angle between u and v}[/tex]
[tex](3i+\sqrt{3}j)\cdot (-2i-5j)=\sqrt{9+3}\cdot \sqrt{4+25}\cdot \cos\theta[/tex]
[tex]-6-5\sqrt{3}=\sqrt{348}\cos\theta[/tex]
[tex]\cos\theta=\dfrac{-6-5\sqrt{3}}{\sqrt{348}}[/tex]
[tex]\theta=\cos^{-1}(-0.7859)[/tex]
[tex]\theta=141.8[/tex]
Nearest degree
[tex]\theta=142^\circ[/tex]
Hence, The angle between u and v is 142°
