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# Find the Angle Between Two Vectors → a and → B If | → a | = √ 3 , ∣ ∣ → B ∣ ∣ = 2 and → a ⋅ → B = √ 6 - CBSE (Arts) Class 12 - Mathematics

ConceptMultiplication of a Vector by a Scalar

#### Question

Find the angle between two vectors $\vec{a} \text{ and } \vec{b}$ if

$\left| \vec{a} \right| = \sqrt{3}, \left| \vec{b} \right| = 2 \text{ and } \vec{a} \cdot \vec{b} = \sqrt{6}$

#### Solution

Let θ be the angle between $\vec{a} \text{ and }\vec{b} .$

Given that

$\left| \vec{a} \right| = \sqrt{3}, \left| \vec{b} \right| = \text{ 2 and }\vec{a} . \vec{b} = \sqrt{6} . . . \left( 1 \right)$
We know that

$\vec{a} . \vec{b} = \left| \vec{a} \right| \left| \vec{b} \right| \cos \theta$

$\Rightarrow \sqrt{6} = \left( \sqrt{3} \right)\left( 2 \right) \cos \theta .....................\left[ \text{ Using }\left( 1 \right) \right]$

$\Rightarrow \cos \theta = \frac{\sqrt{6}}{2\sqrt{3}} = \frac{1}{\sqrt{2}}$

$\Rightarrow \theta = \cos^{- 1} \left( \frac{1}{\sqrt{2}} \right) = \frac{\pi}{4}$

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#### Video TutorialsVIEW ALL [1]

Solution Find the Angle Between Two Vectors → a and → B If | → a | = √ 3 , ∣ ∣ → B ∣ ∣ = 2 and → a ⋅ → B = √ 6 Concept: Multiplication of a Vector by a Scalar.
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