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

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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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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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