Mathematics: Find the angle between vector u= 3i + sqrt 3j and vector v=-2i-5j to the nearest degree a) 82 degrees b) 38 degrees c) 142 degrees d) 98 degrees

132 milesStep-by-step explanation:...

Find the angle between vector u= 3i + sqrt 3j and

mccauley

10.01.2022

The angle between u and v is 142°

C is correct

Step-by-step explanation:

Given: $\vec{u}=3i+\sqrt{3}j$

$\vec{v}=-2i-5j$

We need to find the angle between u and v vector.

Using dot product.

$\vec{u}\cdot \vec{v}=|u||v|\cos\theta$

where,

$\theta\text{ is angle between u and v}$

$(3i+\sqrt{3}j)\cdot (-2i-5j)=\sqrt{9+3}\cdot \sqrt{4+25}\cdot \cos\theta$

$-6-5\sqrt{3}=\sqrt{348}\cos\theta$

$\cos\theta=\dfrac{-6-5\sqrt{3}}{\sqrt{348}}$

$\theta=\cos^{-1}(-0.7859)$

$\theta=141.8$

Nearest degree

$\theta=142^\circ$

Hence, The angle between u and v is 142°

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