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# Find the Angle Between the Vectors → a and → B Where → a = ^ I − ^ J and → B = ^ J + ^ K - CBSE (Arts) Class 12 - Mathematics

ConceptBasic Concepts of Vector Algebra

#### Question

Find the angle between the vectors $\vec{a} \text{ and } \vec{b}$ where $\vec{a} = \hat{i} - \hat{j} \text{ and } \vec{b} = \hat{j} + \hat{k}$

#### Solution

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

$\left| \vec{a} \right| = \sqrt{\left( 1 \right)^2 + \left( - 1 \right)^2} = \sqrt{2}$

$\left| \vec{b} \right| = \sqrt{\left( 1 \right)^2 + \left( 1 \right)^2} = \sqrt{2}$

$\vec{a} . \vec{b} = 0 - 1 + 0 = - 1$

$\cos \theta = \frac{\vec{a} . \vec{b}}{\left| \vec{a} \right| \left| \vec{b} \right|} = \frac{- 1}{\sqrt{2}\sqrt{2}} = \frac{- 1}{2}$

$\Rightarrow \theta = \cos^{- 1} \left( \frac{- 1}{2} \right) = \frac{2\pi}{3}$

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#### Video TutorialsVIEW ALL [4]

Solution Find the Angle Between the Vectors → a and → B Where → a = ^ I − ^ J and → B = ^ J + ^ K Concept: Basic Concepts of Vector Algebra.
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