The angle between two vectors a and b with magnitudes 3 and 4, respectively and a · b = 2 3 is:

Question

The angle between two vectors $\vec{a}$ and $\vec{b}$ with magnitudes $\sqrt{3}$ and 4, respectively and $\vec{a} \cdot \vec{b} = 2 \sqrt{3}$ is:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{π}{3}$

Explanation:

Here, $| \vec{a} |$ $= \sqrt{3},$ $| \vec{b} |$ $= 4$ and $\vec{a} \cdot \vec{b} = 2 \sqrt{3}$ [given]

We know that,

$\vec{a} \cdot \vec{b} =$ $| \vec{a} |$ $| \vec{b} |$ $\cos θ$

$\Rightarrow$ $2 \sqrt{3} = \sqrt{3} \cdot 4 \cdot \cos θ$

$\Rightarrow$ $\cos θ = \frac{2 \sqrt{3}}{4 \sqrt{3}} = \frac{1}{2}$

$∴$ $θ = \frac{π}{3}$

Want Us to Email you About Special Offers & Updates?